A spectral interpretation for the zeros of the Riemann zeta function

Details A spectral interpretation for the zeros of the Riemann zeta function A spectral interpretation for the zeros of the Riemann zeta function

2004-12-14

arxiv.org/abs/math/0412277v2

Mathematisches Institut, Georg-August-Universit\"at G\"ottingen: Seminars Winter Term 2004/2005, Universit\"atsdrucke G\"ottin

Mathematics

Number Theory

15 pages. The second version only differs in typographical matters and an updated reference list

Scientific paper

Based on work of Alain Connes, I have constructed a spectral interpretation
for zeros of L-functions. Here we specialise this construction to the Riemann
zeta function. We construct an operator on a nuclear Frechet space whose
spectrum is the set of non-trivial zeros of zeta. We exhibit the explicit
formula for the zeros of the Riemann zeta function as a character formula.

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