The Riemann Zeta-function: The Theory of the Riemann Zeta-function with ApplicationsThis book provides both classical and new results in Reimann Zeta-Function theory, one of the most important problems in analytic number theory. These results have application in solving problems in multiplicative number theory, such as power moments, the zero-free region, and the zero density estimates. The book also furnishes annotated proofs, end-of-chapter notes, historical discussions and references. |
Contents
ELEMENTARY THEORY | 1 |
EXPONENTIAL INTEGRALS | 55 |
THE VORONOI SUMMATION FORMULA | 83 |
Copyright | |
17 other sections not shown
Common terms and phrases
² dt a₁ a₂ analogous analytic continuation applications approximate functional equation asymptotic formula Atkinson's formula C₁ Cauchy-Schwarz inequality Chapter constant converges Corollary D. R. Heath-Brown defined denote E. C. Titchmarsh error term exponent pairs exponential sums fixed integer follows G. H. Hardy given gives hence Hölder's inequality holds I₁ interval inversion formula J. E. Littlewood J₁ Jutila Lemma Lindelöf hypothesis log log log2T logT M₁ M₂ main term Math mean value method N₁ number theory O(log obtain P₁ partial summation pole power moments prime number theorem Proof of Lemma proof of Theorem proved R₁ R₂ real numbers replaced residue result Riemann hypothesis right-hand side S₁ S₂ satisfy Section summation formula t₁ Theorem 7.2 trivially uniformly upper bounds Voronoi Y₁ zero-free region zeta-function theory Σ Σ Ση