The Theory of the Riemann Zeta-functionClarendon Press, 1986 - 412 páginas The 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. |
Índice
Secção 1_ | 1 |
Secção 2_ | 13 |
Secção 3_ | 45 |
Secção 4_ | 71 |
Secção 5_ | 95 |
Secção 6_ | 119 |
Secção 7_ | 138 |
Secção 8_ | 184 |
Secção 10_ | 254 |
Secção 11_ | 292 |
Secção 12_ | 312 |
Secção 13_ | 328 |
Secção 14_ | 336 |
Secção 15_ | 388 |
| 392 | |
Secção 9_ | 210 |
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Palavras e frases frequentes
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