Hostname: page-component-784d4fb959-9bxm5 Total loading time: 0 Render date: 2025-07-15T17:37:16.494Z Has data issue: false hasContentIssue false
  • English
  • Français

The values of ternary quadratic forms at prime arguments

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  26 February 2010

Glyn Harman
Glyn Harman
Affiliation:
Department of Mathematics, Royal Holloway, University of London, EGHAM, Surrey TW20 0EX, E-mail: G.Harman@rhul.ac.uk
Get access

Extract

For the purpose of this paper, we call a set of positive reals ν a well-spaced set if there is a c > 0 such that

MSC classification

Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes

Information

Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 83 - 96
Copyright
Copyright © University College London 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Baker, R. C. and Harman, G.. Diophantine approximation by prime numbers. J. London Math. Soc. (2), 25 (1982), 201–215.CrossRefGoogle Scholar
2.Baker, R. C. and Harman, G.. On the distribution of αpk modulo one. Mathematika. 38 (1991). 170–184.CrossRefGoogle Scholar
3.Baker, R. C., Harman, G. and Pintz, J.. The exceptional set for Goldbach's problem in short intervals. Sieve Methods, Exponential Sums and their Applications in Number Theory (ed. Greaves, G. R. H., Harman, G. and Huxley, M. N.). Cambridge University Press (1996), 1–54.Google Scholar
4.Cook, R. J. and Fox, A.. The values of ternary quadratic forms at prime arguments. Mathematika, 48 (2001), 137–149.CrossRefGoogle Scholar
5.Davenport, H. and Heilbronn, H.. On indefinite quadratic forms in live variables. J. London Math. Soc., 21 (1946), 185–193.CrossRefGoogle Scholar
6.Ghosh, A.. The distribution of αp2 modulo 1. Proc. London Math. Soc. (3), 42 (1981), 252–269.CrossRefGoogle Scholar
7.Harman, G.. Trigonometric sums over primes I. Mathematika, 28 (1981), 249–254.CrossRefGoogle Scholar
8.Harman, G.. On the distribution of αp modulo one II. Proc. London Math. Soc. (3), 72 (1996). 241–260.CrossRefGoogle Scholar
9.Huxley, M. N.. On the difference between consecutive primes. Invent. Math., 15 (1972). 155–164.Google Scholar
10.Kumchev, A. V.. On Weyl sums over primes and almost primes. Michigan Math. J. (to appear).Google Scholar
11.Landau, E.. Über einige Summen, die von Nullstellen der Riemann'schen Zetafunction abhängen. Ada Math., 35 (1912), 271–294.Google Scholar
12.Titchmarsh, E. C.. Theory of the Riemann Zeta-function (second edition revised by Heath-Brown, D. R.). Clarendon Press (Oxford, 1986).Google Scholar
13.Vaughan, R. C.. Diophantine approximation by prime numbers II. Proc. London Math. Soc. (3), 28 (1974), 385–401.CrossRefGoogle Scholar
14.Vaughan, R. C.. The Hardy Littlewood Method. Cambridge Tracts in Mathematics 80. (Cambridge University Press 1981).Google Scholar
15.Watson, G. L.. On indefinite quadratic forms in five variables. Proc. London Math. Soc. (3). 3 (1953), 170–181.CrossRefGoogle Scholar