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The prime number theorem and Selbergs method
5 The order of magnitude of the divisor function
19 other sections not shown
absolute constant Annals of Math Arithmetical Functions author's Introduction C. L. Siegel Cauchy's theorem Chandrasekharan choose consider converges absolutely converges uniformly Corollary deduce defined denotes the number derived differentiation Dirichlet series divisor divisor function entire function estimate exists finite fixed following Theorem Fourier series functional equation G. H. Hardy given half-plane Hence hypothesis implies inequality Ingham Ingham's Tract interval ip modulo J. E. Littlewood L-functions Landau Landau's Vorlesungen Lemma Littlewood's theorem loglog logx modular transformation non-principal character modulo non-real zeros Notes on Chapter number of solutions number of zeros obtain partial summation periodic function positive integer prime number theorem proof of Theorem proper character Raghavan Narasimhan Ramanujan real axis rectangle regular result Riemann Riemann hypothesis Riemann-von Mangoldt formula right-hand side Satz sufficiently large Titchmarsh's Zeta-function trigonometric uniformly equiconvergent uniformly for a'^x^b Vinogradov's