Analytic Number Theory
Cambridge University Press, Oct 16, 1997 - Mathematics - 382 pages
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.
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1 Subvarieties of Linear Tori and the Unit Equation A Survey
2 Remarks on the Analytic Complexity of Zeta Functions
3 Normal Distribution of Zeta Functions and Applications
4 Goldbach Numbers and Uniform Distribution
5 The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number ...
6 The BrunTitchmarsh Theorem
7 A Decomposition of Riemanns ZetaFunction
8 Multiplicative Properties of Consecutive Integers
14 The Goldbach Problem with Primes in Arithmetic Progressions
15 On the Sum of Three Squares of Primes
16 Trace Formula over the Hyperbolic Upper Half Space
17 Modular Forms and the Chebotarev Density Theorem II
18 Congruences between Modular Forms
19 Regular Singularities in GFunction Theory
20 Spectral Theory and Lfunctions
21 Irrationality Criteria for Numbers of Mahlers Type
9 On the Equation xm lx 1 yq with x Power
10 Congruence Families of Exponential Sums
11 On Some Results Concerning the Riemann Hypothesis
12 Mean Values of Dirichlet Series via Laplace Transforms
13 The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem ...
22 Hypergeometric Functions and Irrationality Measures
23 Forms in Many Variables
24 Remark on the Kuznetsov Trace Formula
absolutely convergent algebraic numbers analogous Analytic Number Theory approximate functional equation approximations argument assume asymptotic Bombieri coefﬁcients completes the proof complex computable congruence conjecture conjugacy class consider convergence Corollary critical line cusp forms deduce deﬁned deﬁnition denote density Diophantine Dirichlet series divisor problem error term estimate exists exponential sums factor ﬁnd ﬁnite ﬁrst ﬁxed follows Fourier functional equation functions f Goldbach h-length Hence holds holomorphic hypergeometric hypothesis implies inequality inﬁnitely interval irrationality measure L-functions L-series Lemma linear lower bound main term Math mean value Mellin transform method minor arcs modular forms modulo Motohashi multiplicative non-negative integers notation number ﬁeld number of solutions obtain polynomial positive integers prime Proc proof of Theorem proved rational numbers result Riemann Hypothesis Riemann zeta function Riemann zeta-function satisﬁes satisfying Selberg sequence sieve spectral Suppose trace formula transform tuple upper bound variables zeta function