A Spectral Interpretation for the Zeros of the Riemann Zeta Function
نویسنده
چکیده
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 ζ-function. We construct an operator on a nuclear Fréchet space whose spectrum is the set of non-trivial zeros of ζ. We exhibit the explicit formula for the zeros of the Riemann ζ-function as a character formula.
منابع مشابه
Spectral analysis and the Riemann hypothesis
The explicit formulas of Riemann and Guinand-Weil relate the set of prime numbers with the set of nontrivial zeros of the zeta function of Riemann. We recall Alain Connes’ spectral interpretation of the critical zeros of the Riemann zeta function as eigenvalues of the absorption spectrum of an unbounded operator in a suitable Hilbert space. We then give a spectral interpretation of the zeros of...
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