Pith. sign in

REVIEW 2 cited by

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

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/9811068 v1 pith:CDPSMHO7 submitted 1998-11-10 math.NT math.CA

classification math.NTmath.CA
keywords formulariemanntracezerosfunctiongiveinterpretationnoncommutative
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. M\"obius randomness in the Hartle-Hawking state

    hep-th 2025-05 unverdicted novelty 7.0 of 10

    The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius avera...

  2. Equivalent Hamiltonian approach to quantum cosmology of integrable models

    gr-qc 2019-08 conditional novelty 5.0 of 10

    For two integrable minisuperspace cosmologies, the paper constructs equivalent Hamiltonians via Faddeev-Jackiw reduction and uses them to study quantum wave packets and Wigner functions.

Pith tools