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

• A. Connes ^[1]
  1. [1] Collège de France

     Collège de France

     París, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 5, Nº. 1, 1999, págs. 29-106
• Idioma: inglés
• DOI: 10.1007/s000290050042
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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 δ of our previous approach.