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 leading international figures in this area, which encompasses the main branches of analytic number theory. In particular, many of the papers reflect the interaction among the different fields of sieve theory, Dirichlet series (including the Riemann Zeta-function), and exponential sums, while 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.
Author(s): G. R. H. Greaves, G. Harman, M. N. Huxley
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1997
Language: English
Pages: 357
Cover......Page 1
Series Titles......Page 2
Title Page......Page 4
Copyright page......Page 5
Contents......Page 6
Foreword......Page 8
Index of Authors......Page 9
Participants in the Symposium......Page 12
1. The Exceptional Set for Goldbach's Problem in Short Intervals......Page 14
2. On an Additive Property of Stable Sets......Page 68
3. Squarefree Values of Polynomials and the abc-Conjecture......Page 78
4 . The Values of Binary Linear Forms ad Prime Arguments......Page 100
5. Some Applications of Sieves of Dimension exceeding 1......Page 114
6. Representations by the Determinant and Mean Values of L-Functions......Page 122
7. On the Montgomery-Hooley Asymptotic Formula......Page 130
8. Franel Integrals......Page 156
9. Eratosthenes, Legendre, Vinogradov and beyond......Page 174
10. On Hypothesis K* in Waring's Problem......Page 188
11. Moments of Differences between Square-free Numbers......Page 200
12. On the Ternary Additive Divisor Problem and the Sixth Moment of the Zeta-Function......Page 218
13. A Variant of the Circle Method......Page 258
14. The Resemblance of the Behaviour of the Remainder Terms E^t), Ai_215. A Note on the Number of Divisors of Quadratic Polynomials......Page 288
16. On the Distribution of Integer Points in the Real Locus of an Afflne Toric Variety......Page 296
17. An Asymptotic Expansion of the Square of the Riemann Zeta-Function......Page 306
18. The Mean Square of Dedekind Zeta-Functions of Quadratic Number Fields......Page 322
19. Artin's Conjecture and Elliptic Analogues......Page 338
