Related papers: A Generalisation of Goursat's Algorithm for Integr…

Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the…

In this paper we revisit the following inverse problem: given a curve invariant under an irreducible finite linear algebraic group, can we construct an ordinary linear differential equation whose Schwarz map parametrizes it? We present an…

We seek discrete approximations to solutions $u:\Omega \to R$ of semilinear elliptic partial differential equations of the form $\Delta u + f_s(u) = 0$, where $f_s$ is a one-parameter family of nonlinear functions and $\Omega$ is a domain…

In this paper we prove a general theorem about congruences between automorphic forms on a reductive group G which is compact at infinity modulo the center. If the rank is one, this essentially reduces to Ribet's level-raising theorem. We…

Let $f(x)$ be a degree $(2g+1)$ monic polynomial with coefficients in an algebraically closed field $K$ with $char(K)\ne 2$ and without repeated roots. Let $\mathfrak{R}\subset K$ be the $(2g+1)$-element set of roots of $f(x)$. Let…

In this paper we consider the degeneracies of the third type. More exact, the perturbations of the Darboux integrable foliation with a triple point, i.e. the case where three of the curves $\{P_i = 0\}$ meet at one point, are considered.…

For a cuspidal automorphic representation of GL2/Q associated to a modular form, the local and global Langlands correspondences are compatible at all finite places of Q. On the p-adic Coleman-Mazur eigencurve this principle can fail (away…

Motivated by the necessity to find exact solutions with the elliptic Weierstrass function of the Einstein's equations (see gr-qc/0105022),the present paper develops further the proposed approach in hep-th/0107231, concerning the s.c. cubic…

The integral Burau representation provides a map from the braid group into a group of integral matrices. This allows for a definition of congruence subgroups of the braid group as the preimage of the usual principal congruence subgroups of…

Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. Let $Aut(X)$ be the group of all automorphisms of $X$ which fix…

Let C be a smooth, projective and geometrically integral curve defined over a finite field F. For each closed point P of C, let R be the ring of functions that are regular outside P, and let K be the completion at P of the function field of…

In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,…

All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is…

The Stable Reduction Theorem guarantees that any smooth, projective, geometrically irreducible curve of genus $g \geq 2$ over a discretely valued field admits a unique stable model after a finite field extension. Computing this model is a…

In this work, the infinite GMRES algorithm, recently proposed by Correnty et al., is employed in contour integral-based nonlinear eigensolvers, avoiding the computation of costly factorizations at each quadrature node to solve the linear…

If $X'= ({\mathbb B} / \Gamma)'$ is a torsion free toroidal compactification of a discrete ball quotient $X_o={\mathbb B} / \Gamma$ and $\xi : (X', T = X'\setminus X_o) \rightarrow (X, D = \xi (T))$ is the blow-down of the $(-1)$-curves to…

Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…

We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…

This work contains two papers: the first published in 2022 and entitled "On the nature of some Euler's double equations equivalent to Fermat's last theorem" provides a marvellous proof through the so-called discordant forms of appropriate…

A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…