Introduction to analytic number theory

By: Apostol, Tom MMaterial type: TextTextSeries: Undergraduate texts in mathematicsPublication details: New Delhi: Narosa, 1998Description: xii, 338 pagesISBN: 9780387901633; 0387901639 ; 9788185015125 ; 8185015120Subject(s): Mathematics | Number theoryDDC classification: 512.73
Contents:
The fundamental theorem of arithmetic -- Arithmetical functions and Dirichlet multiplication -- Averages of arithmetical functions -- Some elementary theorems on the distribution of prime numbers -- Congruences -- Finite abelian groups and their characters -- Dirichlet's theorem on primes in arithmetic progressions -- Periodic arithmetical functions and Gauss sums -- Quadratic residues and the quadratic reciprocity law -- Primitive roots -- Dirichlet series and Euler products -- The functions [Zeta](s) and L(s, [Chi]) -- Analytic proof of the prime number theorem -- Partitions.
Summary: "This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory.
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"First volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology" and continued by the author's Modular functions and Dirichlet series in number theory.

The fundamental theorem of arithmetic --
Arithmetical functions and Dirichlet multiplication --
Averages of arithmetical functions --
Some elementary theorems on the distribution of prime numbers --
Congruences --
Finite abelian groups and their characters --
Dirichlet's theorem on primes in arithmetic progressions --
Periodic arithmetical functions and Gauss sums --
Quadratic residues and the quadratic reciprocity law --
Primitive roots --
Dirichlet series and Euler products --
The functions [Zeta](s) and L(s, [Chi]) --
Analytic proof of the prime number theorem --
Partitions.

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory.

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