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.
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