Zobrazeno 1 - 10
of 156
pro vyhledávání: '"Consani, Caterina"'
We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set $S$ of places of $\mathbb Q$ containing the archimedean place. The measure is given by the abso
Externí odkaz:
http://arxiv.org/abs/2403.01247
Autor:
Connes, Alain, Consani, Caterina
We show that the scaling site $X_{\mathbb Q}$ and its periodic orbits $C_p$ of length $\log p$ offer a geometric framework for the well-known analogy between primes and knots. The role of the maximal abelian cover of $X_{\mathbb Q}$ is played by the
Externí odkaz:
http://arxiv.org/abs/2401.08401
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 analogue of the prolate wave operator. The latter plays a key role bo
Externí odkaz:
http://arxiv.org/abs/2310.18423
Autor:
Connes, Alain, Consani, Caterina
In the present paper, dedicated to Yuri Manin, we investigate the general notion of rings of $\mathbb S[\mu_{n,+}]$-polynomials and relate this concept to the known notion of number systems. The Riemann-Roch theorem for the ring $\mathbb Z$ of the in
Externí odkaz:
http://arxiv.org/abs/2307.06748
Autor:
Connes, Alain, Consani, Caterina
We show that by working over the absolute base $\mathbb S$ (the categorical version of the sphere spectrum) instead of $\mathbb S[\pm 1]$ improves our previous Riemann-Roch formula for $\overline{{\rm Spec\,}\mathbb Z}$. The formula equates the (inte
Externí odkaz:
http://arxiv.org/abs/2306.00456
Autor:
Connes, Alain, Consani, Caterina
We give a historical perspective on the role of the cyclic category in the development of cyclic theory. This involves a continuous interplay between the extension in characteristic one and in S-algebras, of the traditional development of cyclic theo
Externí odkaz:
http://arxiv.org/abs/2208.08339
Autor:
Connes, Alain, Consani, Caterina
In this paper we consider two spectral realizations of the zeros of the Riemann zeta function. The first one involves all non-trivial (non-real) zeros and is expressed in terms of a Laplacian intimately related to the prolate wave operator. The secon
Externí odkaz:
http://arxiv.org/abs/2207.10419
Autor:
Connes, Alain, Consani, Caterina
We prove a Riemann-Roch theorem of an entirely novel nature for divisors on the Arakelov compactification of the algebraic spectrum of the integers. This result relies on the introduction of three key concepts: the cohomologies (attached to a divisor
Externí odkaz:
http://arxiv.org/abs/2205.01391
Autor:
Connes, Alain, Consani, Caterina
We give a short survey on several developments on the BC-system, the adele class space of the rationals, and on the understanding of the "zeta sector" of the latter space as the Scaling Site. The new result that we present concerns the description of
Externí odkaz:
http://arxiv.org/abs/2112.08820
Autor:
Connes, Alain, Consani, Caterina
We exhibit very small eigenvalues of the quadratic form associated to the Weil explicit formulas restricted to test functions whose support is within a fixed interval with upper bound S. We show both numerically and conceptually that the associated e
Externí odkaz:
http://arxiv.org/abs/2106.01715