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math.NT2025
Zeta Spectral Triples
Alain Connes, Caterina Consani, Henri Moscovici
We propose and investigate a strategy toward a proof of the Riemann Hypothesis based on a spectral realization of its non-trivial zeros. Our approach constructs self-adjoint operat…
math.NT2024
Zeta zeros and prolate wave operators
Alain Connes, Caterina Consani, Henri Moscovici
We integrate in the framework of the semilocal trace formula two recent discoveries on the spectral realization of the zeros of the Riemann zeta function by introducing a semilocal…
math.NT2024
On q-series and the moment problem associated to local factors
Alain Connes, Caterina Consani, Henri Moscovici
We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set of places of $\mathbb…