Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta211 Function

摘要

The authors give a spectral interpretation of the critical zeros of the Riemann211u001ezeta function as an absorption spectrum, while eventual noncritical zeros appear 211u001eas resonances. The authors give a geometric interpretation of the explicit 211u001eformulas of number theory as a trace formula on the noncommutative space of Adele 211u001eclasses. This reduces the Riemann hypothesis to the validity of the trace formul 211u001eand eliminates the parameter of their previous approach.