T. Rivoal

activity

20032026

most citedOn the integrality of the Taylor coefficients of mirror maps

21 citations · 68 across the 29 of their papers we have counts for

collaborators

35 papers

math.NT2026

On the singularities of differential equations satisfied by $E$ -functions

Stéphane Fischler, Tanguy Rivoal

Let $ξ$ be a value, at an algebraic point, of a Siegel $E$ -function. As a special case of a very general interpolation result, we prove that there exists an $E$ -function $f$ such t…

math.NT2025

Zeros of $E$ -functions and of exponential polynomials defined over $Q$

Stéphane Fischler, Tanguy Rivoal

Zeros of Bessel functions $J_{α}$ play an important role in physics. They are a motivation for studying zeros of exponential polynomials defined over $Q$ , and mor…

math.NT2025

A new transcendence measure for the values of the exponential function at algebraic arguments

Stéphane Fischler, Tanguy Rivoal

Let $P \in Z [X] ∖ {0}$ be of degree $δ \geq 1$ and usual height $H \geq 1$ , and let $α \in Q^{*}$ be of degree $d \geq 2$ . Mahler proved in 1931 the follow…

math.NT2025

Arithmetic properties of the Taylor coefficients of differentially algebraic power series

Christian Krattenthaler, Tanguy Rivoal

Let $f = \sum_{n = 0}^{\infty} f_{n} x^{n} \in Q [[x]$ be a solution of an algebraic differential equation $Q (x, y (x), \dots, y^{(k)} (x)) = 0$ , where $Q$ is a multivariate po…

math.NT2024

Transcendence of values of logarithms of $E$ -functions

Stéphane Fischler, Tanguy Rivoal

Let $f$ be an $E$ -function (in Siegel's sense) not of the form $e^{β z}$ , $β \in Q$ , and let $lo g$ denote any fixed determination of the complex logarithm. We fi…

math.CA2024

Representability of G-functions as rational functions in hypergeometric series

Thomas Dreyfus, Tanguy Rivoal

Fresán and Jossen have given a negative answer to a question of Siegel about the representability of every $E$ -function as a polynomial with algebraic coefficients in $E$ -functions…

On the singularities of differential equations satisfied by E-functions

Zeros of E-functions and of exponential polynomials defined over Q​

A new transcendence measure for the values of the exponential function at algebraic arguments

Arithmetic properties of the Taylor coefficients of differentially algebraic power series

Transcendence of values of logarithms of E-functions

Representability of G-functions as rational functions in hypergeometric series

On the singularities of differential equations satisfied by $E$ -functions

Zeros of $E$ -functions and of exponential polynomials defined over $Q$

Transcendence of values of logarithms of $E$ -functions