The distribution of prime numbers / Dimitris Koukoulopoulos.
| Author/creator | Koukoulopoulos, Dimitris, 1984- author. |
| Format | Book |
| Publication | Providence, Rhode Island : American Mathematical Society, [2019] |
| Description | xii, 356 pages ; 26 cm. |
| Subjects |
| Series | Graduate studies in mathematics, 1065-7339 ; 203 Graduate studies in mathematics ; v. 203. ^A347883 |
| Contents | And then there were infinitely many -- Asymptotic estimates -- Combinatorial ways to count primes -- The Dirichlet convolution -- Dirichlet series -- An explicit formula for counting primes -- The Riemann zeta function -- The Perron inversion formula -- The prime number theorem -- Dirichlet characters -- Fourier analysis on finite Abelian groups -- Dirichlet L-functions -- The prime number theorem for arithmetic progressions -- Primes and multiplicative functions -- Evolution of sums of multiplicative functions -- The distribution of multiplicative functions -- Large deviations -- Twin primes -- The axioms of Sieve theory -- The fundamental lemma of Sieve theory -- Applications of Sieve methods -- Selberg's Sieve -- Sieving for zero-free regions -- Vinogradov's method -- Ternary arithmetic progressions -- Bilinear forms and the large sieve -- The Bombieri-Vinogradov theorem -- The least prime in an arithmetic progression -- Small gaps between primes -- Large gaps between primes -- Irregularities in the distribution of primes. |
| Bibliography note | Includes bibliographical references and index. |
| LCCN | 2019028661 |
| ISBN | 9781470447540 (hardcover) |
| ISBN | 1470447541 (hardcover) |
| ISBN | (ebook) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Joyner | General Stacks | QA246 .K68 2019 | ✔ Available | Place Hold |