The Distribution of Prime Numbers
Originally published in 1934 in the Cambridge Tracts this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. The major part of the book is devoted to the analytical theory founded on the zeta-function of Riemann. Despite being long out of print, this Tract still remains unsurpassed as an introduction to the field, combining an economy of detail with a clarity of exposition which eases the novice into this area.
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absolutely convergent analytic function applications argument asymptotic bounded Cauchy's theorem Chapter Chebyshev circle complex variable consecutive primes deduce defined denote difference between consecutive Diophantine approximation Dirichlet's series distribution of primes domain elementary equivalent Euler's identity exists explicit formula finite number fixed positive number follows from Theorem footnote functional equation G. H. Hardy Hadamard half-plane Hardy and Littlewood Hence implies inequality infer Ingham integral function integrand interval ir(x Landau Lemma limit log log log loga logarithmic Math maximum modulus principle method multiplicative notation number of primes obtain Pintz points pole with residue positive integers prime number theorem problem properties real axis relation Riemann hypothesis s-plane satisfies Selberg series or integral sieve theory simple pole sufficiently large summation suppose Theorem 19 Theorem 25 Theorem 34 Theorem F theory of primes Titchmarsh tract TT(X uniformly convergent Weierstrass's zeta-function