Analytic Number Theory, Volume 177
Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author's heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdös-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A "Natural" Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem - all presented in a surprisingly elegant and efficient manner with clever examples and interesting problems in each chapter. This text is suitable for a graduate course in analytic number theory.
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afﬁne property analysis analytic function analytic number theory approximation arithmetic progression asymptotic formula Cauchy Chapter common difference complex numbers conclude constant contour integral convergence Crazy Dice cubes deduce deﬁne deﬁnition denote derivatives Dirichlet series e(xnk elementary elements equal Erd6s Euler’s example expressing fact factorization fﬁcients ﬁnal ﬁnally ﬁnd ﬁrst ﬁx ﬁxed forn fourth powers gives inequality inﬁnite integral method L-series lattice point leads Lemma log(N logarithm multiply natural proof nonnegative coefﬁcients nonnegative integers nth powers observation obtain odds order count Parseval partial sums polynomial positive integer power series Prime Number Theorem problem prove question representation functions result Riemann Riemann integral roots of unity satisﬁes series with nonnegative simple subset sum of distinct Thereby trivial unit circle upper bound w)NZ Weyl sums zero zome