Analytic Number Theory
American Mathematical Society (Verlag)
978-1-4704-6770-8 (ISBN)
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques.
The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercises in each section serve a dual purpose, with some intended to improve the reader's understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much necessary information about them included in two survey chapters.
Henryk Iwaniec, Rutgers University, Piscataway, NJ. Emmanuel Kowalski, Universite Bordeaux I, Talence, France.
Introduction
Arithmetic functions
Elementary theory of prime numbers
Characters
Summation formulas
Classical analytic theory of $L$-functions
Elementary sieve methods
Bilinear forms and the large sieve
Exponential sums
The Dirichlet polynomials
Zero-density estimates
Sums over finite fields
Character sums
Sums over primes
Holomorphic modular forms
Spectral theory of automorphic forms
Sums of Kloosterman sums
Primes in arithmetic progressions
The least prime in an arithmetic progression
The Goldbach problem
The circle method
Equidistribution
Imaginary quadratic fields
Effective bounds for the class number
The critical zeros of the Riemann zeta function
The spacing of zeros of the Riemann zeta-function
Central values of $L$-functions
Bibliography
Index
| Erscheinungsdatum | 01.12.2021 |
|---|---|
| Reihe/Serie | Colloquium Publications |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 1-4704-6770-4 / 1470467704 |
| ISBN-13 | 978-1-4704-6770-8 / 9781470467708 |
| Zustand | Neuware |
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