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The distribution of prime numbers / Dimitris Koukoulopoulos.
Math/Physics/Astronomy Library QA246 .K68 2019
Available
- Format:
- Book
- Author/Creator:
- Koukoulopoulos, Dimitris, 1984- author.
- Series:
- Graduate studies in mathematics ; v. 203.
- Graduate studies in mathematics, 1065-7339 ; 203
- Language:
- English
- Subjects (All):
- Numbers, Prime.
- Physical Description:
- xii, 356 pages ; 26 cm.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2019]
- 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.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 9781470447540
- 1470447541
- OCLC:
- 1113143297
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