Analytic Number Theory: An Introductory Course
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/
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2erofree 2eros of 2eta absolute convergence ac(F analytic function approximation argument arithmetic function assertion assume asymptotic bounded character modulo Chebyshev's completely multiplicative constant continuous contour convolution Corollary deduce define denote Dirichlet series error term establish Euler Euler product example exists F and G factor finite number follows Fourier function F functional equation G. H. Hardy generali2ation given half plane hence holds hypothesis implies inequality interval inversion formula ip(x last integral Let F log log logx Math monotone multiplicative function n<x n<x non2ero nonnegative Notes number theory obtain Perron formula positive integer positive number power series prime number prime powers Problem proof of Theorem proved quadratic residue real number rectangle relation residue classes result Riemann-Stieltjes integrals satisfying Selberg's formula sequence si2e sieve squarefree summatory function Suppose tp(x trigonometric polynomial twin primes u)du uniformly Wiener-Ikehara theorem