Sieve Methods, Exponential Sums, and their Applications in Number Theory: (Series Number 237 London Mathematical Society Lecture Note Series)

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.

Table of Contents:
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.