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· 제목 : Lectures on the Riemann Zeta Function (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470418519
· 쪽수 : 119쪽
· 출판일 : 2014-10-30
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470418519
· 쪽수 : 119쪽
· 출판일 : 2014-10-30
목차
- Classical topics
- Panorama of arithmetic functions
- Sums of basic arithmetic functions
- Tchebyshev's prime seeds
- Elementary prime number theorem
- The Riemann memoir
- The analytic continuation
- The functional equation
- The product formula over the zeros
- The asymptotic formula for N(T)
- The asymptotic formula for ?(x)
- The zero-free region and the PNT
- Approximate functional equations
- The Dirichlet polynomials
- Zeros off the critical line
- Zeros on the critical line
- The critical zeros after Levinson
- Introduction
- Detecting critical zeros
- Conrey's construction
- The argument variations
- Attaching a mollifier
- The Littlewood lemma
- The principal inequality
- Positive proportion of the critical zeros
- The first moment of Dirichlet polynomials
- The second moment of Dirichlet polynomials
- The diagonal terms
- The off-diagonal terms
- Conclusion
- Computations and the optimal mollifier
- Smooth bump functions
- The gamma function
- Bibliography
- Index
