Diophantine properties of numbers related to Catalan's constant
- T. Rivoal, W. Zudilin
- Mathematics
- 16 May 2003
1) as a linear form in 1 and even beta valuesonly. The following Lemma 2 is almost the same as the correspondingone in [BR] and we only include a sketch of the proof. We would like toemphasise the…
On the integrality of the Taylor coefficients of mirror maps
- C. Krattenthaler, T. Rivoal
- Mathematics
- 10 September 2007
We show that the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$ are integers, where ${\bf F}(z)$ and ${\bf G}(z)+\log(z) {\bf F}(z)$ are specific solutions of certain…
An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series
- C. Krattenthaler, T. Rivoal
- Mathematics
- 8 December 2003
We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple integral. This integral generalizes integrals of Vasilenko and Vasilyev…
On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps
- E. Delaygue, T. Rivoal, J. Roques
- Mathematics
- 23 September 2013
Using Dwork's theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. This enables us to prove certain p-adic congruences for the generalized hypergeometric series…
Irrationality measures for some automatic real numbers
- B. Adamczewski, T. Rivoal
- MathematicsMathematical Proceedings of the Cambridge…
- 10 June 2009
Abstract This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive…
Rational approximations for values of derivatives of the Gamma function
- T. Rivoal
- Mathematics
- 25 June 2009
The arithmetic nature of Euler's constant γ is still unknown and even getting good rational approximations to it is difficult. Recently, Aptekarev managed to find a third order linear recurrence with…
Nombres D’Euler, approximants de Padé et constante de Catalan
- T. Rivoal
- Mathematics
- 1 April 2006
RésuméAu moyen d’une méthode d’approximation de Padé introduite par Prévost dans [13], nous construisons des familles d’approximations rationnelles rapidement convergentes vers la constante de…
ON THE BITS COUNTING FUNCTION OF REAL NUMBERS
- T. Rivoal
- MathematicsJournal of the Australian Mathematical Society
- 1 August 2008
Abstract Let Bn(x) denote the number of 1’s occurring in the binary expansion of an irrational number x>0. A difficult problem is to provide nontrivial lower bounds for Bn(x) for interesting numbers…
Remainder Pade Approximants for the Exponential Function
- M. Prévost, T. Rivoal
- Mathematics
- 2007
Following our earlier research, we propose a new method for obtaining the complete Pade table of the exponential function. It is based on an explicit construction of certain Pade approximants, not…
Rational approximation to values of G-functions, and their expansions in integer bases
- S. Fischler, T. Rivoal
- Mathematics
- 21 December 2015
We prove a general effective result concerning approximation of irrational values at rational points a / b of any G-function F with rational Taylor coefficients by fractions of the form $$n/(B\cdot…
...
...