Analytic Number Theory

Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.

Yoichi Motohashi (Edited by)

9780521625128, Cambridge University Press

Paperback, published 16 October 1997

396 pages, 1 b/w illus.
22.9 x 15.2 x 2.2 cm, 0.52 kg

' … 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

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.

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.

Subject Areas: Number theory [PBH]