Titlebook: Basic Analytic Number Theory; Anatolij A. Karatsuba,Melvyn B. Nathanson Book 1993 Springer-Verlag Berlin Heidelberg 1993 Analytic Number T

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Integer Points,In this chapter we consider two fundamental problems in the theory of integer points: Gauss’s problem on the number of integer points inside a circle, and the Dirichlet divisor problem. We shall assume that a Cartesian coordinate (.) system has been defined on the plane.

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Entire Functions of Finite Order,This chapter provides background information from the theory of entire functions that will be used later in the book.

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The Euler Gamma Function,The Euler gamma function . is defined by the equation.where . is Euler’s constant.

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The Riemann Zeta Function,For Re . 1, the.is defined by.It follows from the definition that ζ(s) is an analytic function in the half-plane Re . > 1.

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