Related papers: Mahler series with multiplicative coefficient sequ…

Let $\MCZK$, denote the multiplier algebra over $\CZK$, the algebra of continuous functions into the compact operators with spectrum the infinite product of two-spheres. We consider multiplier projections in $\MCZK$ of a certain diagonal…

In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized…

Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take into account some congruence properties of successive…

In this article we prove a generalization of the Bloch-Wigner exact sequence over commutative rings with many units. When the ring is a domain, we get a generalization of Suslin's Bloch-Wigner exact sequence over infinite fields. Our proof…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

We prove that a multiplicative function $f:\mathbb{N}\to\mathbb{C}$ is Toeplitz if and only if there are a Dirichlet character $\chi$ and a finite subset $F$ of prime numbers such that $f(n)=\chi(n)$ for each $n$ which is coprime to all…

In 1923 Schur considered the following problem. Let f(X) be a polynomial with integer coefficients that induces a bijection on the residue fields Z/pZ for infinitely many primes p. His conjecture, that such polynomials are compositions of…

For each positive characteristic multiple zeta value (defined by Thakur), the first and third authors constructed a $t$-module together with an algebraic point such that a specified coordinate of the logarithmic vector of the algebraic…

Consider partial maps from the free monoid into the field of real numbers with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus…

We provide a characterization of infinite algebraic Galois extensions of the rationals with uniformly bounded local degrees, giving a detailed proof of all the results announced in a paper by Checcoli and Zannier and obtaining relevant…

We prove a few uniform versions of the Mordell-Lang Conjecture and of the Shafarevich Conjecture for curves over function fields and their rational points. The main focus is on function fields having high transcendence degree over the…

We derive lower und upper bounds for the degree of regularity of an overdetermined, zero-dimensional and homogeneous quadratic semi-regular system of polynomial equations. The analysis is based on the interpretation of the associated…

We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous…

We focus on combinatorial aspects of the Hilbert series of the cohomology ring of the moduli space of stable pointed curves of genus zero. We show its graded Hilbert series satisfies an integral operator identity. This is used to give…

The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…

In this paper, we introduce product-wise generalizations of certain Marczewski-Burstin bases, including sets with the (s)-property and completely Ramsey sets. For each of these families, we establish analogs of the classical Luzin and…

The notion of $b$-regular sequences was generalized to abstract numeration systems by Maes and Rigo in 2002. Their definition is based on a notion of $\mathcal{S}$-kernel that extends that of $b$-kernel. However, this definition does not…

Let k be an algebraically closed field of characteristic p. Let X(p^e;N) be the curve parameterizing elliptic curves with full level N structure (where p does not divide N) and full level p^e Igusa structure. By modular curve, we mean a…

We study the Euler characteristic of the real Milnor fibres of a real analytic map, using a relation between complex monodromy and complex conjugation. We deduce the result of Coste and Kurdyka that the Euler characteristic of the link of…

We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and…