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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…
math.NT2024
Knots, Primes and the adele class space
Alain Connes, Caterina Consani
We show that the scaling site and its periodic orbits of length offer a geometric framework for the well-known analogy between primes and knots. The…