Complex Analysis in Number Theory

Karatsuba/, Anatoly A.

The Complex Integration Method and Its Application in Number Theory, Generating Functions in Number Theory, Summation Formula, Riemann's Zeta-Function and Its Simplest Properties, The Theory of Riemann's Zeta-Function, Zeros on the Critical Line, The Boundary of Zeros, Approximate Equations of the z(s) Function, The Method of Trigonometric Sums in the Theory of the z(s) Function, Density Theorems, The Order of Growth of |z(s)| in a Critical Strip, Universal Properties of the z(s) Function, Riemann's Hypothesis, Its Equivalents, Computations, Dirichlet L-Functions: Dirichlet's Characters, Dirichlet L-Functions and Prime Numbers in Arithmetic Progressions, Zeros of L-Functions, Real Zeros of L-Functions and the Number of Classes of Binary Quadratic Forms, Density Theorems, L-Functions and Nonresidues, Approximate Equations, On Primitive Roots, References, Author Index, Subject Index