The Theory of the Riemann Zeta-functionThe Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis. |
Contents
Section 1 | 1 |
Section 2 | 13 |
Section 3 | 45 |
Section 4 | 71 |
Section 5 | 95 |
Section 6 | 119 |
Section 7 | 138 |
Section 8 | 184 |
Section 10 | 254 |
Section 11 | 292 |
Section 12 | 312 |
Section 13 | 328 |
Section 14 | 336 |
Section 15 | 388 |
| 392 | |
Section 9 | 210 |
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Common terms and phrases
1+it 2+iT analytic apply approximate argument bound centre chapter circle condition consider constant contains continuous convergent corresponding critical deduce defined denote depends easily equal error estimate example fact factor finite fixed formula functional equation given gives greater Hence holds improved inequality infinity integral interval least Lemma less Littlewood loglog Math mean method multiplicity O(log o+it obtain particular points pole positive possible prime problem proof prove Putting rectangle region regular relation replaced residues respect result follows Riemann hypothesis right-hand side satisfies similar Similarly strip sufficient Suppose tends term theorem theory Titchmarsh true uniformly values write zeros zeta-function Σ Σ ΣΣ