# 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={A. Connes},
journal={Selecta Mathematica},
year={1998},
volume={5},
pages={29-106}
}
• A. Connes
• Published 1998
• Mathematics
• Selecta Mathematica
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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