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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.NT2025
Knots, primes and class field theory
Alain Connes, Caterina Consani
In this paper, we present a geometric generalization of class field theory, demonstrating how adelic constructions, central to the spectral realization of zeros of L-functions and…