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greaves g sieve methods exponential sums app number theory 1997

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Textbook in PDF format 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. Foreword Index of Authors Participants in the Symposium The Exceptional Set for Goldbach's Problem in Short Intervals R.C. Baker, G. Harman and J. Pintz On an Additive Property of Stable Sets A. Balog and I.Z. Ruzsa Squarefree Values of Polynomials and the abc-Conjecture J. Browkin, M. Filaseta, G. Greaves and A. Schinzel The Values of Binary Linear Forms ad Prime Arguments J. Brudern, R.J. Cook and A. Perelli Some Applications of Sieves of Dimension exceeding 1 H. Diamond and H. Halberstam Representations by the Determinant and Mean Values of L-Functions W. Duke, J. Friedlander and H. Iwanie On the Montgomery-Hooley Asymptotic Formula D.A. Goldston and R.C. Vaughan Franel Integrals R.R. Hall Eratosthenes, Legendre, Vinogradov and beyond G. Harman On Hypothesis K* in Waring's Problem C. Hooley Moments of Differences between Square-free Numbers M.N. Huxley On the Ternary Additive Divisor Problem and the Sixth Moment of the Zeta-Function A. Ivić A Variant of the Circle Method M. Jutila The Resemblance of the Behaviour of the Remainder Terms Eσ(t), Δ1-σ(x) and R(σ+it) I. Kiuchi and K. Matsumoto A Note on the Number of Divisors of Quadratic Polynomials J. McKee On the Distribution of Integer Points in the Real Locus of an Afflne Toric Variety B.Z. Moroz An Asymptotic Expansion of the Square of the Riemann Zeta-Function Y. Motohashi The Mean Square of Dedekind Zeta-Functions of Quadratic Number Fields Y. Motohashi Artin's Conjecture and Elliptic Analogues M. jr. Murty

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greaves g sieve methods exponential sums app number theory 1997