Analytic Number Theory

ISBN-13: 9780521625128 / Angielski / Miękka / 1997 / 396 str.

Y. Motohashi

Opis

This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and diophantine approximations and equations. This will be a valuable book for graduates and researchers working in number theory.

Recenzje

' … an authoritative, up-to-date review of analytic number theory. This will be a valuable book for graduates and researchers working in number theory.' L'Enseignement Mathématique

Spis treści

Foreword; Speakers; 1. Subvarieties of linear tori and the unit equation A survey E. Bombieri; 2. Remarks on the analytic complexity of zeta functions E. Bombieri; 3. Normal distribution of zeta functions and applications E. Bombieri and A. Perelli; 4. Goldbach numbers and uniform distribution J. Brüdern and A. Perelli; 5. The number of algebraic numbers of given degree approximating a given algebraic number J.-H. Evertse; 6. The Brun–Titchmarsh theorem J. Friedlander and H. Iwaniec; 7. A decomposition of Riemann's Zeta function A. Granville; 8. Multiplicative properties of consecutive integers A. J. Hildebrand; 9. On the equation (x^m - 1)/(x - 1) = y^q with x power N. Hirata-Kohno and T. N. Shorey; 10. Congruence families of exponential sums M. N. Huxley and N. Watt; 11. On some results concerning the Riemann hypothesis A. Ivic; 12. Mean values of Dirichlet series via Laplace transforms M. Jutila; 13. The mean square of the error term in a generalization of the Dirichlet divisor problem K.-Y. Lam and K.-M. Tsang; 14. The Goldbach problem with primes in arithmetic progressions M.-C. Liu and T. Zhan; 15. On the sum of three squares of primes H. Mikawa; 16. Trace formula over the hyperbolic upper half space Y. Motohashi; 17. Modular forms and the Chebotarev density theorem II V. K. Murty; 18. Congruences between modular forms M. R. Murty; 19. Regular singularities in G-function theory M. Nagata; 20. Spectral theory and L-functions P. Sarnak; 21. Irrationality criteria for numbers of Mahler's type T. N. Shorey and R. Tijdeman; 22. Hypergeometric functions and irrationality measures C. Viola; 23. Forms in many variables T. D. Woley; 24. Remark on the Kuznetsov trace formula E. Yoshida.