Related papers: Degree 1 elements of the Selberg class

In this paper we study the ratio between the number of $p$-elements and the order of a Sylow $p$-subgroup of a finite group $G$. As well known, this ratio is a positive integer and we conjecture that, for every group $G$, it is at least the…

We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.

As in [5], we study holomorphic maps of positive degree between compact complex manifolds, and prove that any holomorphic map of degree one from a compact complex manifold to itself is biholomorphic. This conclusion confirms that under a…

In a 2008 paper Ellenberg suggested a strategy to improve the known upper bounds for the $\ell$-torsion part of class groups of number fields of fixed degree $d$. Motivated by this he proposed a question about the number of primitive…

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

Given a reductive Lie algebra over the complex numbers, we introduce a family of category which generalises the BGG category $\mathcal{O}$. We also classify the simple modules for some of these categories and prove a semisimplicity result.

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.

We introduce the N\'eron-Severi Lie algebra of a Soergel module and we determine it for a large class of Schubert varieties. This is achieved by investigating which Soergel modules admit a tensor decomposition. We also use the…

We classify simple weight modules with finite-dimensional weight spaces over the (centrally extended complex) Schr\"odinger algebra in (1+1)-dimensional space-time. Our arguments use the description of lowest weight modules by Dobrev,…

We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…

We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.

The purpose of this paper is to describe explicitly the modules of (Siegel-)Jacobi forms of degree two of index one of any scalar valued weight with respect to some congruence subgroups of small levels $N\leq 4$. Such a structure for the…

I describe the history of Topological Tverberg Theorem. I present some important constructions and discuss their properties. In particular, I describe in details the cell structure of the classifying space $K\left( S_{r},1\right),$ where…

We introduce the class of sober rings and investigate it through several key results, highlighting connections to some other known classes of rings. We analyze sufficient conditions for a ring to be sober, as well as necessary conditions.…