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math.NT2023
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.NT2023
On the metaphysics of
Alain Connes, Caterina Consani
In the present paper, dedicated to Yuri Manin, we investigate the general notion of rings of -polynomials and relate this concept to the known notion of number…
math.NT2023
Riemann-Roch for the ring
Alain Connes, Caterina Consani
We show that by working over the absolute base (the categorical version of the sphere spectrum) instead of improves our previous Riemann-Roch formula…