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Zbl 1074.11001
Bateman, Paul T.; Diamond, Harold G.
Analytic number theory. An introductory course. (English)
[B] Monographs in Number Theory 1. River Edge, NJ: World Scientific. xiii, 360~p. \sterling~26.00; \$~42.00 pbk; \sterling~48.00; \$~78.00 hbk (2004). ISBN 981-238-938-5/hbk; ISBN 981-256-080-7/pbk

This textbook steers a gentle course through multiplicative analytic number theory. Beginning with arithmetic functions and their summatory functions, it takes the student through the elementary proof of the prime number theorem (PNT), and then to Dirichlet series, the Wiener-Ikehara proof of the PNT, and then to the classical proof, with de la Vallée-Poussin's error term. One then meets characters, Dirichlet $L$-functions, and the PNT for arithmetic progressions, followed by some simple oscillation theorems. The book concludes with two chapters on sieves. There are exercises scattered throughout the book, and end of chapter notes.\par This book is suitable for beginning graduate students, or possibly even advanced undergraduates.
[Roger Heath-Brown (Oxford)]

MSC 2000:: *11-01 Textbooks (number theory)
11Mxx Analytic theory of zeta and L-functions
11Nxx Multiplicative number theory
11N37 Asymptotic results on arithmetic functions
11N36 Appl. of sieve methods
11N05 Distribution of primes
11M06 Riemannian zeta-function and Dirichlet L-function

Keywords: analytic number theory; arithmetic functions; prime number theorem; Riemann zeta-function; sieves

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