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Number Theory, Fourier Analysis and Geometric Discrepancy
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The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.

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Contents

References
[1] T. van, Aardenne-Ehrenfest, Proof of the impossibility of a just distribution of an infinite sequence of points over an interval, Proc. Kon. Ned. Akad. v. Wetensch 48 (1945), 266–271.
[2] T. van, Aardenne-Ehrenfest, On the impossibility of a just distribution, Proc. Kon. Ned. Akad. v. Wetensch 52 (1949), 734–739.
[3] W.W., Adams, L.J., Goldstein, Introduction to number theory, Prentice-Hall, 1976.
[4] J., Agnew, Explorations in number theory, Contemporary Undergraduate Mathematics Series, Brooks/Cole, 1972.
[5] W.R., Alford, A., Granville, C., Pomerance, There are infinitely many Carmichael numbers, Ann. of Math. 139 (1994), 703–722.
[6] G.E., Andrews, Number theory, Dover Publications, 1994.
[7] G.E., Andrews, S.B., Ekhad, D., Zeilberger, A Short Proof of Jacobi's formula for the number of representations of an integer as a sum of four squares, Amer. Math. Monthly 100 (1993), 274–276.
[8] T.M., Apostol, Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer, 1998.
[9] A., Baker, A concise introduction to the theory of numbers, Cambridge University Press, 1984.
[10] P.T., Bateman, H.G., Diamond, Analytic number theory. An introductory course, World Scientific Publishing, 2004.
[11] D., Bayer, P., Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), 294–313.
[12] J., Beck, Balanced two-colourings of finite sets in the square I, Combinatorica 1 (1981), 50–64.
[13] J., Beck, Irregularities of distribution I, Acta Math. 159 (1987), 1–49.
[14] J., Beck, W.W.L., Chen, Irregularities of distribution, Cambridge Tracts in Mathematics, 89, Cambridge University Press, 2008.
[15] J., Beck, W.W.L., Chen, Note on irregularities of distribution II, Proc. London Math. Soc. 61 (1990), 251–272.
[16] D.R., Bellhouse, Area estimation by point counting techniques, Biometrics 37 (1981), 303–312.
[17] F., Benford, The law of anomalous numbers, Proc. Am. Philos. Soc. 78 (1938), 551–572.
[18] A., Berger, T.P., Hill, Benford's law strikes back: no simple explanation in sight for mathematical gem, Math. Intelligencer 33 (2011), 85–91.
[19] D., Bilyk, Roth's orthogonal functions method in discrepancy theory and some new connections, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Sri-vastav, G., Travaglini - Editors), Lecture Notes in Mathematics, Springer, to appear.
[20] S., Bochner, The role of mathematics in the rise of science, Princeton University Press, 1966.
[21] E., Borel, Les probabilités denombrables et leurs applications arithmétiques, Rend. Circ. Mat. Palermo 27 (1909), 247–271.
[22] L., Brandolini, W.W.L., Chen, L., Colzani, G., Gigante, G., Travaglini, Discrepancy and numerical integration in Sobolev spaces on metric measures spaces, preprint.
[23] L., Brandolini, W.W.L., Chen, G., Gigante, G., Travaglini, Discrepancy for randomized Riemann sums, Proc. Amer. Math. Soc. 137 (2009), 3177–3185.
[24] L., Brandolini, C., Choirat, L., Colzani, G., Gigante, R., Seri, G., Travaglini, Quadrature rules and distribution of points on manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear
[25] L., Brandolini, L., Colzani, G., Gigante, G., Travaglini, On the Koksma-Hlawka inequality, J. Complexity 29 (2013), 158–172.
[26] L., Brandolini, L., Colzani, G., Gigante, G., Travaglini, A Koksma-Hlawka inequality for simplices, in ‘Trends in harmonic analysis’ (M., Picardello - Editor), Springer INd AM Series, Springer, 2013, 33–46.
[27] L., Brandolini, L., Colzani, A., Iosevich, A., Podkorytov, G., Travaglini, Geometry of the Gauss map and lattice points in convex domains, Mathematika 48 (2001), 107–117.
[28] L., Brandolini, L., Colzani, G., Travaglini, Average decay of Fourier transforms and integer points in polyhedra, Ark. Mat. 35 (1997), 253–275.
[29] L., Brandolini, G., Gigante, S., Thangavelu, G., Travaglini, Convolution operators deined by singular measures on the motion group, Indiana Univ. Math. J. 59 (2010), 1935–1945.
[30] L., Brandolini, G., Gigante, G., Travaglini, Irregularities of distribution and average decay of Fourier transforms, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear
[31] L., Brandolini, A., Greenleaf, G., Travaglini, Lp – Lp′ estimates for overdetermined Radon transforms, Trans. Amer. Math. Soc. 359 (2007), 2559–2575.
[32] L., Brandolini, S., Hofmann, A., Iosevich, Sharp rate of average decay of the Fourier transform of a bounded set, Geom. Funct. Anal. 13 (2003), 671–680.
[33] L., Brandolini, A., Iosevich, G., Travaglini, Spherical means and the restriction phenomenon, J. Fourier Anal. Appl. 7 (2001), 359–372.
[34] L., Brandolini, A., Iosevich, G., Travaglini, Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution, Trans. Amer. Math. Soc. 355 (2003), 3513–3535.
[35] L., Brandolini, M., Rigoli, G., Travaglini, Average decay of Fourier transforms and geometry ofconvexsets, Rev. Mat. Iberoamer. 14 (1998), 519–560.
[36] L., Brandolini, G., Travaglini, Pointwise convergence of Fejér type means, Tohoku Math. J. 49 (1997), 323–336.
[37] L., Brandolini, G., Travaglini, La legge di Benford, Emmeciquadro 45 (2012).
[38] J., Bruna, A., Nagel, S., Wainger, Convex hypersurfaces and Fourier transforms, Ann. of Math. 127 (1988), 333–365.
[39] F., Cantelli, Sulla probabilità come limite della frequenza, Atti Accad. Naz. Lincei 26 (1917), 39–45.
[40] J.W.S., Cassels, On the sums of powers of complexnumbers, Acta Math. Hungar. 7 (1957), 283–289.
[41] D.G., Champernowne, The construction of decimal normal in the scale of ten, J. London Math. Soc. 8 (1933), 254–260.
[42] K., Chandrasekharan, Introduction to analytic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 148, Springer, 1968.
[43] B., Chazelle, The discrepancy method. Randomness and complexity, Cambridge University Press, 2000.
[44] W.W.L., Chen, On irregularities of distribution III, J. Austr. Math. Soc. 60 (1996), 228–244.
[45] W.W.L., Chen, Lectures on irregularities of point distribution, unpublished, 2000.
[46] W.W.L., Chen, Elementary number theory, unpublished, 2003.
[47] W.W.L., Chen, Fourier techniques in the theory of irregularities of point distribution, in ‘Fourier analysis and convexity’ (L., Brandolini, L., Colzani, A., Iosevich, G., Travaglini - Editors), Birkhauser, 2004, 59–82.
[48] W.W.L., Chen, M., Skriganov, Upper bounds in irregularities of point distribution, in “Apanorama of discrepancy theory” (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear.
[49] W.W.L., Chen, A., Srivastav, G., Travaglini - Editors, A panorama of discrepancy theory, Lecture Notes in Mathematics, Springer, to appear.
[50] W.W.L., Chen, G., Travaglini, Discrepancy with respect to convex polygons, J. Complexity 23 (2007), 662–672.
[51] W.W.L., Chen, G., Travaglini, Deterministic and probabilistic discrepancies, Ark. Mat. 47 (2009), 273–293.
[52] W.W.L., Chen, G., Travaglini, Some of Roth's ideas in discrepancy theory, in ‘Analytic number theory: essays in honour of Klaus Roth’ (W.W.L., Chen, W.T., Gowers, H., Halberstam, W.M., Schmidt, R.C., Vaughan – Editors), Cambridge University Press, 2009, 150–163.
[53] P.R., Chernoff, Pointwise convergence of Fourier series, Amer. Math. Monthly 87 (1980),399–400.
[54] K.L., Chung, A course in probability theory, Academic Press, 2001.
[55] M., Cipolla, Sui numeri composti Pcheveriicano la congruenza di Fermat ap-1 ≡ 1 (mod P), Ann. Mat. Pura Appl. 9 (1904), 139–160.
[56] J.A., Clarkson, On the series of prime reciprocals, Proc. Amer. Math. Soc. 17 (1966), 541.
[57] L., Colzani, G., Gigante, Summation formulas and integer points under shifted generalized hyperbolae, preprint.
[58] L., Colzani, G., Gigante, G., Travaglini, Trigonometric approximation and a general form of the Erdos-Turán inequality, Trans. Amer. Math. Soc. 363 (2011), 1101–1123.
[59] L., Colzani, G., Gigante, G., Travaglini, Unpublished, 2012.
[60] L., Colzani, I., Rocco, G., Travaglini, Quadratic estimates for the number of integer points in convex bodies, Rend. Circ. Mat. Palermo 54 (2005), 241–252.
[61] J.H., Conway, R.K., Guy, The book of numbers, Copernicus, 1996.
[62] A.H., Copeland, P., Erdos, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857–860.
[63] W.A., Coppel, Number theory. An introduction to mathematics, Springer, 2009.
[64] J.G. van der, Corput, Zalhentheorische abschätzungen, Math. Ann. 84 (1921), 53–79.
[65] J.G. van der, Corput, Zalhentheorische abschätzungen mit anwendung auf gitter-punktprobleme, Math. Z. 17 (1923), 250–259.
[66] J.G. van der, Corput, Verteilungsfunktionen I-VIII, Proc. Akad. Amsterdam 38 (1935), 813–821, 1058-1066; 39 (1936), 10-19, 19-26, 149-153, 339-344, 489-494, 579-590.
[67] H., Davenport, Notes on irregularities of distribution, Mathematika 3 (1956), 131–135.
[68] J. De, Koninck, F., Luca, Analytic number theory. Exploring the anatomy of integers. Graduate Studies in Mathematics, 134, American Mathematical Society, 2012.
[69] P., Diaconis, The distribution of leading digits and uniform distribution mod 1, Ann. Prob. 5 (1977), 72–81.
[70] P., Diaconis, D., Freedman, On rounding percentages, J. Amer. Statist. Assoc. 366 (1979), 359–364.
[71] J., Dick, F., Pillichshammer, Discrepancy theory and quasi-Monte Carlo integration, in ‘A panorama of discrepancy theory’ (W.W.L., Chen, A., Srivastav, G., Travaglini – Editors), Lecture Notes in Mathematics, Springer, to appear.
[72] L.E., Dickson, History of the theory of numbers, Vol. I, II, Chelsea Publishing Co., 1966.
[73] M., Drmota, R.F., Tichy, Sequences, discrepancies and applications. Lecture Notes in Mathematics, 1651, Springer, 1997.
[74] P., Erdos, On almost primes, Amer. Math. Monthly 57 (1950), 404–407.
[75] P., Erdos, W.H.J., Fuchs, On a problem of additive number theory, J. London Math. Soc. 31 (1956), 67–73.
[76] P., Erdos, J., Suranyi, Topics in the theory of numbers, Undergraduate Texts in Mathematics, Springer, 2003.
[77] P., Erdos, P., Turan, On a problem in the theory of uniform distribution I, II, Indag. Math. 10 (1948), 370-378, 406–413.
[78] G., Everest, T., Ward, An introduction to number theory, Graduate Texts in Mathematics, 232, Springer, 2005.
[79] D.E., Flath, Introduction to number theory, John Wiley & Sons, 1989.
[80] B., Flehinger, On the probability that a random integer has initial digit A, Amer. Math. Monthly 73 (1966), 1056–1061.
[81] G.B., Folland, Fourier analysis and its applications, Wadsworth & Brooks/Cole, 1992.
[82] G.B., Folland, Real analysis. Modern techniques and their applications, John Wiley & Sons, 1999.
[83] L.J., Goldstein, A history of the prime number theorem, Amer. Math. Monthly 80 (1973), 599–615.
[84] S.W., Graham, G., Kolesnik, Van der Corput's method of exponential sums, London Mathematical Society Lecture Note Series, 126, Cambridge University Press, 1991.
[85] A., Granville, The Fundamental theorem of arithmetic, preprint.
[86] A., Granville, Z., Rudnick – Editors, Equidistribution in number theory, an introduction, Springer, 2007
[87] T.H., Gronwall, Some asymptotic expressions in the theory of numbers, Trans. Amer. Math. Soc. 14 (1913), 113–122.
[88] G.H., Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. 46 (1915), 263–283.
[89] G.H., Hardy, On Dirichlet's divisor problem, Proc. London Math. Soc. 15 (1916), 1–25.
[90] G.H., Hardy, E.M., Wright, An introduction to the theory of numbers, Oxford University Press, 1938.
[91] G., Harman, Metric number theory, London Mathematical Society Monographs, New Series, 18, Oxford University Press, 1998.
[92] G., Harman, Variations on the Koksma-Hlawka inequality, Unif. Distr. Theory 5 (2010), 65–78.
[93] H., Hasse, Number theory, Springer, 1980.
[94] F.J., Hickernell, Koksma-Hlawka inequality, in ‘Encyclopedia of statistical sciences’ (S., Kotz, C.B., Read, D.L., Banks - Editors), Wiley-Interscience, 2006.
[95] E., Hlawka, The theory of uniform distribution, AB Academic Publishers, 1984.
[96] E., Hlawka, J., Schoißengeier, R., Taschner, Geometric and analytic number theory, Universitext, Springer, 1991.
[97] P., Hoffman, The man who loved only numbers: The story of Paul Erdos and the search for mathematical truth, Hyperion Books, 1998.
[98] L.K., Hua, Introduction to number theory, Springer, 1982.
[99] M.N., Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523–531.
[100] M.N., Huxley, Area, lattice points and exponential sums, London Mathematical Society Monographs, New Series, 13, Oxford Science Publications, 1996.
[101] K., Ireland, M., Rosen, A classical introduction to modern number theory, Graduate Texts in Mathematics, 84, Springer, 1990.
[102] A., Ivic, The Riemann zeta-function. Theory and applications, Dover Publications, 2003.
[103] G.A., Jones, J.M., Jones, Elementary number theory, Springer Undergraduate Mathematics Series, Springer, 1998.
[104] C., Joy, P.P., Boyle, K.S., Tan, Quasi-Monte Carlo methods in inance, Management Science 42 (1996), 926–938.
[105] Y., Katznelson, An introduction to harmonic analysis, Cambridge Mathematical Library, Cambridge University Press, 2004.
[106] D.G., Kendall, On the number of lattice points in a random oval, Quart. J. Math. Oxford Series 19 (1948), 1–26.
[107] N., Koblitz, A course in number theory and cryptography, Graduate Texts in Mathematics, 114, Springer, 1994.
[108] H., Koch, Number theory, Graduate Studies in Mathematics, American Mathematical Society, 2000.
[109] J.F., Koksma, Een algemeene stellinguit de theorie der gelijkmatige verdeeling modulo 1, Mathematica B (Zupten) 11 (1942–43), 7–11.
[110] T., Kollig, A., Keller, Efficient multidimensional sampling, Computer Graphics Forum 21 (2002), 557–563.
[111] M.N., Kolountzakis, T., Wolff, On the Steinhaus tiling problem, Mathematika 46 (1999), 253–280.
[112] S.V., Konyagin, M.M., Skriganov, A.V., Sobolev, On a lattice point problem arising in the spectral analysis of periodic operators, Mathematika 50 (2003), 87–98.
[113] E., Kratzel, Lattice points, Mathematics and its Applications, Kluwer Academic Publisher, 1988.
[114] L., Kuipers, H., Niederreiter, Uniform distribution of sequences, Dover Publications, 2006.
[115] E., Landau, Über die gitterpunkte in einen kreise (Erste, zweite Mitteilung), Nachr. K. Gesellschaft Wiss. Gottingen, Math.-Phys. Klasse (1915), 148-160, 161–171.
[116] E., Landau, ber Dirichlets teilerproblem, Sitzungsber, Math.-Phys. Klasse Knigl. Bayer. Akad. Wiss. (1915), 317–328.
[117] N.N., Lebedev, Special functions and their applications, Dover Publication, 1972.
[118] F., Lemmermeyer, Reciprocity laws (from Euler to Eisenstein), Springer Monographs in Mathematics, Springer, 2000.
[119] W.J., LeVeque, Fundamentals of number theory, Addison-Wesley, 1977.
[120] W.J., LeVeque, Elementary theory of numbers, Dover Publications, 1990.
[121] J., Matousek, Geometric discrepancy. An illustrated guide, Algorithms and Combinatorics, 18, Springer, 2010.
[122] R., Matthews, The power of one, New Scientist, 10 July 1999.
[123] H., Montgomery, Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Regional Conference Series in Mathematics, 84, American Mathematical Society, 1994.
[124] W.J., Morokoff, R.E., Caflisch, A quasi-Monte Carlo approach to particle simulation of the heat equation, SIAM J. Numer. Anal. 30 (1993), 1558–1573.
[125] R.M., Murty, N., Thain, Prime numbers in certain arithmetic progressions, Funct. Approx. Comment. Math. 35 (2006), 249–259.
[126] R.M., Murty, N., Thain, Pick's theorem via Minkowski's theorem, Amer. Math. Monthly 114 (2007), 732–736.
[127] W., Narkiewicz, Number theory, World Scientific, 1983.
[128] M.B., Nathanson, Elementary methods in number theory, Graduate Texts in Mathematics, 195, Springer, 2000.
[129] S., Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), 39–40.
[130] D.J., Newman, A simplified proof of the Erdos-Fuchs theorem, Proc. Amer. Math. Soc. 75 (1979), 209–210.
[131] H., Niederreiter, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, 63, SIAM, 1992.
[132] M., Nigrini, Benford's law. Applications for forensic accounting, Auditing, and fraud detection, John Wiley & Sons, 2012.
[133] M., Nigrini, L., Mittermaier, The use of Benford's law as an aid in analytical procedures, Auditing – A Journal of Practice & Theory 16 (1997), 52–67.
[134] I., Niven, Irrational numbers, Carus Mathematical Monographs, 11, MAA, 2005.
[135] I., Niven, H., Zuckerman, An introduction to the theory of numbers, John Wiley & Sons, 1980.
[136] O., Ore, Number theory and its history, Dover Publications, 1988.
[137] L., Parnovski, N., Sidorova, Critical dimensions for counting lattice points in Euclidean annuli. Math. Model. Nat. Phenom. 5 (2010), 293–316.
[138] L., Parnovski, A., Sobolev, On the Bethe-Sommerfeld conjecture for the polyharmonic operator, Duke Math. J. 107 (2001), 209–238.
[139] R., Pinkham, On the distribution of first significant digits, Ann. Math. Stat. 32 (1961), 1223–1230.
[140] M.A., Pinsky, Introduction to Fourier analysis and wavelets, Graduate Studies in Mathematics, 102, American Mathematical Society, 2002.
[141] M., Plancherel, Contribution a l'etude de la representation d'une fonction arbitraire par les integrales definies, Rend. del Circ. Mat. Palermo 30 (1910), 298–335.
[142] A.N., Podkorytov, The asymptotic of a Fourier transform on a convex curve, Vestn. Leningr. Univ. Mat. 24 (1991), 57–65.
[143] S., Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc. 11 (1919), 181–182.
[144] B., Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139, 271–278.
[145] D., Redmond, Number theory. An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 201, Marcel Dekker, 1996.
[146] E., Regazzini, Probability and statistics in Italy during the First World War I: Cantelli and the laws of large numbers, J. Electron. Hist. Probab. Stat. 1 (2005) 1–12.
[147] F., Ricci, G., Travaglini, Convex curves, Radon transforms and convolution operators defined by singular measures, Proc. Amer. Math. Soc. 129 (2001), 1739–1744.
[148] S., Robinson, Still guarding secrets after years of attacks, RSA earns accolades for its founders, SIAM News 36 5 (2003).
[149] K.F., Roth, On irregularities of distribution, Mathematika 1 (1954), 73–79.
[150] W., Rudin, Principles of mathematical analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, 1976.
[151] J.D., Sally, P.J., Sally, Roots to research. A vertical development of mathematical problems, American Mathematical Society, 2007.
[152] W.M., Schmidt, Irregularities of distribution IV, Invent. Math. 7 (1968), 55–82.
[153] W.M., Schmidt, Lectures on irregularities of distribution, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 56, Tata Institute of Fundamental Research, Bombay, 1977.
[154] E., Scholz (Editor), Hermann Weyl's Raum-Zeit-Materie and a general introduction to his scientific work, DMV Seminar 30, Birkhauser, 2001.
[155] W., Sierpinski, O Pewnem zagadnieniu zrachunku funckcy asymptotycznych, Prace mat.-fiz. 17 (1906), 77–118.
[156] R.A., Silverman, Complex analysis with applications, Dover Publications, 1984.
[157] S., Singh, The code book: The science of secrecy from ancient Egypt to quantum cryptography, Doubleday Books, 1999.
[158] I.H., Sloan, H., Wozniakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?J. Complexity 14 (1998), 1–33.
[159] P., Soardi, Serie di Fourier in più variabili, Unione Matematica Italiana -Pitagora, Quaderni dell'Unione Matematica Italiana 26, 1984.
[160] C.D., Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, 105, Cambridge University Press, 1993.
[161] E., Stein, R., Shakarchi, Fourier analysis, An introduction, Princeton Lectures in Analysis, I, Princeton University Press, 2003.
[162] E., Stein, R., Shakarchi, Real analysis, Measure theory, integration, and Hilbert spaces, Princeton Lectures in Analysis, III, Princeton University Press, 2005.
[163] E., Stein, R., Shakarchi, Functional analysis, Princeton Lectures in Analysis IV, Princeton University Press, 2011.
[164] E., Stein, G., Weiss, Introduction to Fourier analysis in Euclidean spaces, Princeton Mathematical Series, 32, Princeton University Press, 1971.
[165] I.N., Stewart, D.O., Tall, Algebraic number theory, Chapman and Hall Mathematics Series, Chapman and Hall, 1979.
[166] J., Stillwell, Elements of algebra, Geometry, numbers, equations, Undergraduate Texts in Mathematics, Springer, 1994.
[167] J., Stillwell, Elements of number theory, Undergraduate Texts in Mathematics, Springer, 2003.
[168] D.R., Stinson, Cryptography, Theory and practice, CRC Press Series on Discrete Mathematics and its Applications, Chapman & Hall/CRC, 2002.
[169] M., Tarnopolska-Weiss, On the number of lattice points in planar domains, Proc. Amer. Math. Soc. 69 (1978), 308–311.
[170] G., Travaglini, Fejer kernels for Fourier series on Tn and on compact Lie groups, Math. Z. 216 (1994), 265–281.
[171] G., Travaglini, Crittograia, Emmeciquadro 21 (2004), 21–28.
[172] G., Travaglini, Average decay of the Fourier transform, in ‘Fourier analysis and convexity’ (L., Brandolini, L., Colzani, A., Iosevich, G., Travaglini – Editors), Birkhauser, 2004, 245–268.
[173] G., Travaglini, Appunti su teoria dei numeri, analisi di Fouriere distribuzione di punti, Unione Matematica Italiana – Pitagora, Quaderni dell'Unione Matematica Italiana 52, 2010.
[174] K., Tsang, Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function, Sci. China Math. 53 (2010), 2561–2572.
[175] M., Tupputi, in preparation.
[176] J.D., Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183–216.
[177] G., Voronoï, Sur un problème du calcul des fonctions asymptotiques, J. Reine Angew. Math. 126 (1903), 241–282.
[178] G.N., Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, 1922.
[179] D.D., Wall, Normal numbers, Thesis, University of California, 1949.
[180] H., Weyl, Über ein problem aus dem gebiete der diophantischen approximationen, Nacr. Ges. Wiss. Gottingen (1914), 234–244.
[181] H., Weyl, Über die gleichverteilung von zhalen mod. eins, Math. Ann. 77 (1916), 313–352.
[182] R.L., Wheeden, A., Zygmund, Measure and integral. An introduction to real analysis, Pure and Applied Mathematics, 43, Marcel Dekker, 1977.
[183] Y., Zhang, Bounded gaps between primes, Ann. Math. 179 (2014), 1121–1174.
[184] G., Ziegler, The great prime number record races, Notices Amer. Math. Soc. 51 (2004), 414–416.
[185] A., Zygmund, Trigonometric series, I, II, Cambridge Mathematical Library, Cambridge University Press, 1993.

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