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9781470464448 Academic Inspection Copy

Analytic Number Theory for Beginners

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This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
Prapanpong Pongsriiam, Silpakorn University, Nakhon Pathom, Thailand, and Nagoya University, Japan.
Review of elementary number theory Arithmetic functions I The floor function Summation formulas Arithmetic functions II Elementary results on the distribution of primes Characters and Dirichlet's theorem The Riemann zeta function Prime number theorem and some extensions Introduction to other topics Hints for selected exercises Bibliography Subject index Name Index
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