Report
Rational approximations to values of $E$-functions
| العنوان: | Rational approximations to values of $E$-functions |
|---|---|
| المؤلفون: | Fischler, Stéphane, Rivoal, Tanguy |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11J82 (Primary), 11J91 (Secondary) |
| الوصف: | 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. Comment: 32 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.12043 |
| رقم الانضمام: | edsarx.2312.12043 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |