Topics in Analytic Number Theory

Jason Wanner

ISBN 10: 3845419806 / ISBN 13: 9783845419800

Published by LAP LAMBERT Academic Publishing Jul 2011, 2011

About this Item

Neuware -One can describe Analytic Number Theory informally as being the elegant subject where ideas and concepts from real and complex analysis are applied to number-theoretic problems. This book is an overview of some important results in Analytic Number Theory. Topics include Dirichlet L-series, their analytic continuations and functional equations, including relevant supporting material on characters, Gamma functions and the Riemann Zeta-Function. We also examine Dirichlet's Theorem, giving the existence of infinitely many prime numbers congruent to a given 'a modulo b' when 'a' and 'b' are coprime, the Prime Number Theorem for arithmetic progressions and the Poisson Summation Formula. We then discuss how these ideas can be applied to the theory of the so-called Negative Pell Equation, which is an interesting and unlikely application.Books on Demand GmbH, Überseering 33, 22297 Hamburg 140 pp. Englisch.

Seller Inventory # 9783845419800

Bibliographic Details

• Title: Topics in Analytic Number Theory
• Publisher: LAP LAMBERT Academic Publishing Jul 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3845419806
• ISBN 13: 9783845419800
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

One can describe Analytic Number Theory informally as being the elegant subject where ideas and concepts from real and complex analysis are applied to number-theoretic problems. This book is an overview of some important results in Analytic Number Theory. Topics include Dirichlet L-series, their analytic continuations and functional equations, including relevant supporting material on characters, Gamma functions and the Riemann Zeta-Function. We also examine Dirichlet's Theorem, giving the existence of infinitely many prime numbers congruent to a given "a modulo b" when "a" and "b" are coprime, the Prime Number Theorem for arithmetic progressions and the Poisson Summation Formula. We then discuss how these ideas can be applied to the theory of the so-called Negative Pell Equation, which is an interesting and unlikely application.

About the Author

Jason Wanner obtained a first class degree in mathematics in 2008 and then completed his Masters (by research) degree in pure mathematics in 2010. He currently teaches mathematics to secondary school and sixth form students, and thoroughly enjoys this role.