Multiplicative number theory I Classical theory 1st Edition by Hugh L Montgomery,Robert C Vaughan ISBN 0521849039 9780521849036
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Product details:
ISBN 10: 0521849039
ISBN 13: 9780521849036
Author: Hugh L. Montgomery, Robert C. Vaughan
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular, their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan, Imperial College, London and Pennsylvania State University.
Table of contents:
Chapter 1 Dirichlet Series: I
Chapter 2 The Elementary Theory of Arithmetic Functions
Chapter 3 Principles and First Examples of Sieve Methods
Chapter 4 Primes in Arithmetic Progressions: I
Chapter 5 Dirichlet Series: II
Chapter 6 The Prime Number Theorem
Chapter 7 Applications of the Prime Number Theorem
Chapter 8 Further Discussion of the Prime Number Theorem
Chapter 9 Primitive Characters and Gauss Sums
Chapter 10 Analytic Properties of the Zeta Function and L-Functions
Chapter 11 Primes in Arithmetic Progressions: II
Chapter 12 Explicit Formulae
Chapter 13 Conditional Estimates
Chapter 14 Zeros
Chapter 15 Oscillations of Error Terms
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Tags: Hugh L Montgomery, Robert C Vaughan, Multiplicative Number Theory, Classical Theory