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The Distribution of Prime Numbers
About this Title
Dimitris Koukoulopoulos, Université de Montréal, Montréal, QC, Canada
Publication: Graduate Studies in Mathematics
Publication Year:
2019; Volume 203
ISBNs: 978-1-4704-4754-0 (print); 978-1-4704-5420-3 (online)
DOI: https://doi.org/10.1090/gsm/203
MathSciNet review: MR3971232
MSC: Primary 11N05; Secondary 11-01, 11M06, 11N35, 11N60
Table of Contents
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Front/Back Matter
Chapters
First principles
Methods of complex and harmonic analysis
- 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
Multiplicative functions and the anatomy of integers
- Primes and multiplicative functions
- Evolution of sums of multiplicative functions
- The distribution of multiplicative functions
- Large deviations
Sieve methods
- 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
Bilinear methods
- Vinogradov’s method
- Ternary arithmetic progressions
- Bilinear forms and the large sieve
- The Bombieri-Vinogradov theorem
- The least prime in an arithmetic progression
Local aspects of the distribution of primes
Appendices
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