Related papers: Note on Lisbon integrals and their associated D--m…
We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space $\mathbb{C}^k$ of unitary polynomials $P_s(z)$ where $s\in\mathbb{C}^k$ and $z\in \mathbb{C}$, $s_i$…
In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.
These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to…
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.
The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…
The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.
Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…
The aim of this article is to compare two different definitions of level-structers of Drinfeld modules and to prove that they are equivalent.
This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicitly describe the V-filtration of the mixed twistor D-modules…
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"
The first part of these notes is devoted to an introduction to algebraic $D$-modules. Several basic notions are introduced. In the second part, $D$-modules with group action are treated. Several important examples in this situation are…
The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…
The purpose of this note is to report on recent joint work with J. Funke, P. Jenkins, and K. Ono on the traces of CM values of modular functions and some applications.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We explain a formalism of regular holonomic $D$-modules for algebraic geometers using the distinguished triangles associated with algebraic local cohomology together with meromorphic Deligne extensions of local systems as well as the dual…
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…