In this paper we use the framework of automatic sequences to study combinatorial
sequences modulo prime powers. Given a sequence whose generating function is the …

We show that the n-fold integrals χ (n) of the magnetic susceptibility of the Ising model, as
well as various other n-fold integrals of the'Ising class', or n-fold integrals from enumerative …

Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion
to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the …

Let K be a field of characteristic zero and k and l be two multiplicatively independent positive
integers. We prove the following result that was conjectured by Loxton and van der Poorten …

The various Artin approximation theorems assert the existence of power series solutions of a
certain quality $ Q $(ie, formal, analytic, algebraic) of systems of equations of the same …

We develop a new method for proving algebraic independence of $ G $-functions. Our
approach rests on the following observation: $ G $-functions do not always come with a …

We describe a general method for giving $ p $-adic interpretations of $ G $-functions arising
from degenerating periods of smooth projective algebraic varieties. Using this, we are able …

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics
and enumerative combinatorics. In all the examples emerging from physics, the minimal …

We prove that if y=∑ n= 0∞ a (n) xn∈ F q [[x]] is an algebraic power series of degree d,
height h, and genus g, then the sequence a is generated by an automaton with at most q h+ …

Ce travail est consacré à l'étude de l'algébricité modulo p des G-fonctions de Siegel. Notre
but est de souligner la pertinence de la notion de structure de Frobenius forte …