# Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

@article{Connes1998TraceFI, title={Trace formula in noncommutative geometry and the zeros of the Riemann zeta function}, author={Alain Connes}, journal={Selecta Mathematica}, year={1998}, volume={5}, pages={29-106} }

Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace formula and eliminates the parameter
$ \delta $ of our previous approach.

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