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Pré-Publication, Document De Travail Année : 2023

Rational approximations to values of $E$-functions

Résumé

We solve a long standing problem in the theory of Siegel's $E$-functions, initiated by Lang for Bessel's function $J_0$ in the 60's and considered in full generality by G. Chudnovsky in the 80's: we prove that irrational values taken at rational points by $E$-functions with rational Taylor coefficients have irrationality exponent equal to 2. This result had been obtained before by Zudilin under stronger assumptions on algebraic independence of E-functions, satisfied by $J_0$ but not by all hypergeometric $E$-functions for instance.
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Dates et versions

hal-04349259 , version 1 (17-12-2023)
hal-04349259 , version 2 (10-01-2024)

Identifiants

  • HAL Id : hal-04349259 , version 2

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Stéphane Fischler, Tanguy Rivoal. Rational approximations to values of $E$-functions. 2024. ⟨hal-04349259v2⟩
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