G. R. H. Greaves

Sieve Methods, Exponential Sums, and their Applications in Number Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This volume comprises the proceedings of the 1995 Cardiff symposium on sieve methods, exponential sums, and their applications in number theory. Included are contributions from many leading international figures in this area which encompasses the main branches of analytic number theory. In particular, many of the papers reflect the interaction between the different fields of sieve theory, Dirichlet series (including the Riemann Zeta-function), and exponential sums, whilst displaying the subtle interplay between the additive and multiplicative aspects of the subjects. The fundamental problems discussed include recent work on Waring's problem, primes in arithmetical progressions, Goldbach numbers in short intervals, the ABC conjecture, and the moments of the Riemann Zeta-function.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 30. Januar 1997
• Englisch
• ISBN-13: 9780511893384
• Artikelnr.: 38190160

Inhaltsangabe

1. The exceptional set for Goldbach's problem in short intervals R. C.
Baker, G. Harman and J. Pintz; 2. On an additive property of stable sets A.
Balog and I. Rusza; 3. Squarefree values of polynomials and the
abc-conjecture J. Browkin, M. Filaseta, G. Greaves and A. Schinzel; 4. The
values of binary linear forms at prime arguments J. Brüdern, R. J. Cook and
A. Perelli; 5. Some applications of sieves of dimension exceeding 1 H.
Diamond and H. Halberstam; 6. Representations by the determinant and mean
values of L-functions W. Duke, J. Friedlander and H. Iwaniec; 7. On
Montgomery-Hooley asymptotic formula D. A. Goldston and R. C. Vaughan; 8.
Franel integrals R. R. Hall; 9. Eratosthenes, Legendre, Vinogradov and
beyond G. Harman; 10. On hypothesis K* in Waring's problem C. Hooley; 11.
Moments of differences between square-free numbers M. N. Huxley; 12. On the
ternary additive problem and the sixth moment of the zeta-function A. Ivic;
13. A variant of the circle method M. Jutila; 14. The resemblance of the
behaviour of the remainder terms Es(t), D1-2s(x) and R(s+it) I. Kiuchi and
K. Matsumoto; 15. A note on the number of divisors of quadratic polynomials
J. McKee; 16. On the distribution of integer points in the real locus of an
affine toric variety B. Z. Moroz; 17. An asymptotic expansion of the square
of the Riemann zeta-function Y. Motohashi; 18. The mean square of Dedekind
zeta-functions of quadratic number fields Y. Motohashi; 19. Artin's
conjecture and elliptic analogues M. R. Murty.