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

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dc.creatorConnes, Alain
dc.date1998-11-10
dc.date.accessioned2026-07-07T05:26:49Z
dc.date.available2026-07-07T05:26:49Z
dc.descriptionWe 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.
dc.description88 pages
dc.identifierhttps://arxiv.org/abs/math/9811068
dc.identifierhttp://arxiv.org/abs/math/9811068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77693
dc.subjectNumber Theory
dc.subjectClassical Analysis and ODEs
dc.subject11M
dc.titleTrace formula in noncommutative geometry and the zeros of the Riemann zeta function
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