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Generalised Euler constants

  • J. Knopfmacher (a1)
Abstract

Let the Laurent expansion of the Riemann zeta function ξ(s) about s=1 be written in the form

It has been discovered independently by many authors that, in terms of this notation, the coefficient

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References
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(1) Bateman P. T. and Diamond H. G., Asymptotic distribution of Beurling's general- ized prime numbers, Studies in Number Theory, MAA Studies in Math., Vol. 6 (Prentice-Hall, 1969).
(2) Berndt B. C., On the Hurwitz zeta function. Rocky Mountain J. Math. 2 (1972), 151157.
(3) Berndt B. C., Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications, J. Number Theory 7 (1975), 413445.
(4) Briggs W. E., The irrationality of y or of sets of similar constants, K. Norske Vid. Selsk. Forh. (Trondheim) 34 (1961), 2528.
(5) Briggs W. E.,& Buschman R. G., The power series coefficients of functions defined by Dirichlet series, Illinois J. Math. 5 (1961), 4344.
(6) Briggs W. E. & Chowla S., The power series coefficients of ζ(s), Amer. Math. Monthly 62 (1955), 323325.
(7) Cohen E., On the average number of direct factors of a finite abelian group. Acta Arith. 6 (1960), 159173.
(8) Knopfmacher J., Arithmetical properties of finite rings and algebras, and analytic number theory, I-V, J. Reine Angew. Math. 252 (1972), 1643, 254 (1972), 7499, 259 (1973), 157170, 270 (1974), 97114, 271 (1974), 95121.
(9) Knopfmacher J., Abstract Analytic Number Theory (North-Holland Publ. Co., 1975).
(10) Landau E., Über die zueinem algebraischen Zahlkörper gehörige Zetafunktion …, J. Reine Angew. Math. 125 (1903), 64188.
(11) Landau E., Über eine idealtheoretische Funktion. Trans. Amer. Math. Soc. 13 (1912), 121.
(12) Landau E., Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale (Chelsea Publ. Co., 1949 reprint).
(13) Lehmer D. H., Euler constants for arithmetical progressions, Acta Arith. 27 (1975), 125142.
(14) Siegel C. L., Lectures on Advanced Analytic Number Theory (Tata Inst, of Fund. Research, 1961).
(15) Van Veen S. C., Math. Reviews 29 (1965) #2232.
(16) Widder D. V., The Laplace Transform (Princeton Univ. Press, 1941).
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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