1.4k citations · 8.5k across the 104 of their papers we have counts for
116 papers
On the Absolute Geometry of
Alain Connes, Caterina Consani
A guiding principle in P. Scholze's -adic geometry asserts that the points of over an algebraically closed perfectoid field of characteristic …
On the Jacobian of
Alain Connes, Caterina Consani
We interpret the structure of the adele class space of the rationals--and specifically its Riemann sector--as the natural monoidal extension of the Picard group of the arithmetic c…
The Riemann Hypothesis: Past, Present and a Letter Through Time
Alain Connes
This paper, commissioned as a survey of the Riemann Hypothesis, provides a comprehensive overview of 165 years of mathematical approaches to this fundamental problem, while introdu…
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…
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…
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…