Analytic number theory

Includes bibliography and references.

1 Subvarieties of linear Tori and the unit equation : a survey ;
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 of 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 [superscript m] -1)/(x-1) = y[superscript 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. Ivić
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 the three squares of primes / H. Mikawa
16 Trace formula over the hyberbolic 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. Wooley
24 Remark on the Kuznetsov trace formula / E. Yoshida

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.