Acknowledgments Except for some exercises, I am indebted to the literature of analytic number theory for all the material in this textbook. As references I have chiefly relied on the following works: For arith- metic functions Introduction to Analytic and Probabilistic Number Theory by erald Tenenbaum, and for prime number theory Multiplicative Number Theory I. Classical Theory by Hugh L. Montgomery and Robert C. Vaughan have been the main references. But for an easy proof of the Prime Number Theorem with an error term I have followed The Distribution of Prime Num- bers [Ing90] by A. E. Ingham. For my very modest account of the analytic properties of the Riemann zeta function I am indebted to The Theory of the Riemann Zeta-function [Tit86] by E. C. Titchmarsh. The chapter on the Circle Method owes the most to the second edition of Analytic Methods for Diophantine Equations and Diophantine Inequalities [Dav05] by H. Daven- port, edited by T. D. Browning and with a Foreword by D. E. Freeman, D. R. Heath-Brown and R. C. Vaughan, though in a few particulars I have fol- lowed the treatment in the second edition of The Hardy-Littlewood Method [Vau97] by R. C. Vaughan. For the chapter on the Dedekind zeta func- tion my main sources have been Lectures on Algebraic and Analytic Number Theory [G´ al61] by I. S. al, the contribution by H. A. Heilbronn in the collection Algebraic Number Theory [Hei67] edited by J. W. S. Cassels and A. Fr¨ olich, Algebraic Number Theory [Lan70] by Serge Lang, Elementary and Analytic Theory of Algebraic Numbers [Nar00b] by W. Narkiewicz, Algebraic Number Theory by urgen Neukirch, and especially the exposi- tory articles The Analytic Theory of Algebraic Numbers [Sta75] and Galois Theory, Algebraic Number Theory and Zeta Functions [Sta95] by H. M. Stark. xiii
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