Related papers: Formal conjugacy and asymptotic differential algeb…
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized…
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.
In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincar\'e series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which…
We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.
We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent…
The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of symmetric…
We study certain classes of equations for $F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in contrast to both classical and $p$-adic cases, formal power…
We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $\pi$ induced from an irreducible supercuspidal…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
We discuss the convergence problem for coordinate transformations which take a given vector field into Poincar\'e-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these…
We give an explicit implicit function theorem for formal power series that is valid for all fields, which implies in particular Lagrange inversion formula and and Flajolet-Soria coefficient extraction formula known for fields of…
In the framework of semiclassical resonances, we make more precise the link between polynomial estimates of the extension of the resolvent and propagation of the singularities through the trapped set. This approach makes it possible to…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
Considering supergravity theory is a natural step in the development of gravity models. This paper follows the ``algebraic`` path and constructs possible extensions of the Poincar\'e and Anti-de-Sitter algebras, which inherit their basic…
We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…
We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $GL_n$…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…
We consider a family of holomorphic PDEs whose singular locus is given by the zero set of an analytic map $P$ with $P(0)=0$. Our goal is to establish conditions for the existence and uniqueness of formal power series solutions and to…