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

  title={Trace formula in noncommutative geometry and the zeros of the Riemann zeta function},
  author={Alain Connes},
  journal={Selecta Mathematica},
  • 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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