S. Fischler

activity

20052026

most citedMany odd zeta values are irrational

20 citations · 45 across the 28 of their papers we have counts for

collaborators

37 papers

math.NT2026

The ring of values of $E$ -functions is not a field

Stéphane Fischler, Tanguy Rivoal

Let $E$ be the ring of values taken at algebraic points by $E$ -functions. The exponential function and the Bessel function $J_{0}$ are classical examples of $E$ -functions. W…

math.NT2026

Transcendence measure for the values of the logarithmic derivative of the Bessel function $J_{0}$ 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 $d \geq 2$ . As a consequence of general resu…

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.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…

The ring of values of E-functions is not a field

Transcendence measure for the values of the logarithmic derivative of the Bessel function J0​ at algebraic arguments

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

Transcendence of values of logarithms of E-functions

The ring of values of $E$ -functions is not a field

Transcendence measure for the values of the logarithmic derivative of the Bessel function $J_{0}$ at algebraic arguments

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