Riemann ’ s Explicit / Exact formula
نویسنده
چکیده
The idea is that the equality of the Euler product and Riemann-Hadamard product for zeta allows extraction of an exact formula for a suitably-weighted counting of primes, a sum over zeros of zeta, via a contour integration of the logarithmic derivatives. As observed by [Guinand 1947] and [Weil 1952], [Weil 1972], the classical formulas are equalities of values of a certain distribution, in the sense of generalized functions.
منابع مشابه
Riemann ’ s and ζ ( s )
[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...
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