Related papers: An index theorem for gerbes

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

This is the second paper of a series. It extends the results of the first paper from number fields to finitely generated fields, based on the recent theory of adelic line bundles of the same authors. We prove an arithmetic Hodge index…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…

We prove a version of ergodic theorem for an action of an amenable group, where a F{\o} lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.

In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.

We prove Burkholder inequality using Bregman divergence.

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…

The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.

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.

This paper presents a generalized version of a theorem of Grzegorek and Labuda in category bases and also endeavours to establish a variant formulation of the same in Marczewski structures.

This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.

We give a q-analogue of Gauss' divisibility theorem

A short proof of a theorem of M.H. Albert, and its application to lattices.

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

A proof of Sendov's conjecture is given.

Assuming the Hodge conjecture for abelian varieties of CM-type, one obtains a good category of abelian motives over the algebraic closure of a finite field and a reduction functor to it from the category of CM-motives. Consequentely, one…

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.