Related papers: On the WALA conjecture, Alberti representations an…
The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.
An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…
In this paper, we give a simple counter example to the famous Hodge conjecture.
We use a weight-preserving, sign-reversing involution to find a combinatorial expansion of $\Delta_{e_k} e_n$ at $q=1$ in terms of the elementary symmetric function basis. We then use a weight-preserving bijection to prove the Delta…
We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…
In this paper, we find a new recurrence formula fo the Euler zeta functions.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…
A short proof of a theorem of M.H. Albert, and its application to lattices.
A proof of Sendov's conjecture is given.
In the paper it is reported that Bell's correlation formula allows an Einstein local hidden variables explanation. The key is the application of Petis integration.
We reinterpret a conjecture of Breuil on the locally analytic $\mathrm{Ext}^1$ in a functorial way using $(\varphi,\Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or…
In this article we use the Desargues' theorem and its reciprocal to solve two problems.
In this paper, we proved a special case of the DDVV Conjecture.
This article is a survey about applications of bi-quantization theory in Lie theory. We focus on a conjecture of M. Duflo. Most of the applications are coming from our article with Alberto Cattaneo and some extensions are relating…
We prove several extensions of the Erdos-Fuchs theorem.
An introduction is given to the Littlewood-Richardson rule, and various combinatorial constructions related to it. We present a proof based on tableau switching, dual equivalence, and coplactic operations. We conclude with a section…
We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.
We establish a connection between a function and a series representation using a similar technique with that that Euler used to solve the Basel problem. Our result concerns a more general series from which one can obtain $\zeta(2k)$ as a…
We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.