Theory of Numbers: A Textbook

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Alpha Science International, Jan 1, 2007 - Mathematics - 277 pages
Theory of Numbers: A Textbook is aimed at students of Mathematics who are graduates or even undergraduates. Very little prerequisites are needed. The reader is expected to know the theory of functions of a real variable and in some chapters complex integration and some simple principles of complex function theory are assumed. The entire book is self contained except theorems 7 and 9 of chapter 11 which are assumed. The most ambitious chapter is chapter 11 where the most attractive result on difference between consecutive primes is proved. References to the latest developments like Heath-Brown's work and the work of R.C. Baker, G. Harman and J. Pintz along with readable accounts of Brun's sieve and also of Apery's Theorem on irrationality of zeta (3) are given. Finally the reader is acquainted with Montgomery-Vaughan Theorem in the last chapter. It is hoped that the reader will enjoy the leisurely style of presentation of many important results.

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Contents

Preface vii
1
Simple 1 results based on simple properties s
29
Landaus theorem on the singularity of Dirichlet series
35
Copyright

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