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· 제목 : Analytic Number Theory (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 정수론
· ISBN : 9781470467708
· 쪽수 : 615쪽
· 출판일 : 2021-11-30
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 정수론
· ISBN : 9781470467708
· 쪽수 : 615쪽
· 출판일 : 2021-11-30
목차
- 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
