Related papers: Functorial characterization of Mittag-Leffler modu…
The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…
It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to…
In this paper we introduce a new fractional derivative with respect to another function the so-called $\psi$-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we…
We define two $L$-functions associated to a common vector valued eigenform $f$ transforming with the ``finite'' Weil representation. The first one can be seen as a standard zeta function defined by the eigenvalues of $f$. The second one can…
In this paper, we introduce a new generalized class of analytic functions involving the Mittag-Leffler operator and Bazilevi\u{c} functions. We examine inclusion properties, radius problems and an application of the generalized…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
We define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when…
We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
In this paper, Whittaker modules are studied for a subalgebra $\mathfrak{q}_{\epsilon}$ of the $\emph{N}$=2 superconformal algebra. The Whittaker modules are classified by central characters. Additionally, criteria for the irreducibility of…
We explain some fundamental differences between the theories of mixed Hodge modules and mixed twistor modules (including the difference in weight system on the nearby cycle functor) which do not seem to be clarified explicitly in the…
We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all…
In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.
We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms
We construct two categorifications of the Lusztig--Vogan module associated to a real reductive algebraic group. The first categorification is given by semisimple complexes in an equivariant derived category, and the second is constructed as…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
This article is a research exposition based on the author's talk at the International Colloquium on Automorphic Representations and L-Functions, 2012, held at TIFR, Mumbai. We consider some special cases of the following question: when is a…
The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can be rewritten as a complex contour integral which can be used…