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Diophantine properties of numbers related to Catalan's constant
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 theExpand
On the integrality of the Taylor coefficients of mirror maps
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 certainExpand
Irrationality measures for some automatic real numbers
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 deriveExpand
Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps
We generalise Dwork's theory of $p$-adic formal congruences from the univariate to a multi-variate setting. We apply our results to prove integrality assertions on the Taylor coefficients ofExpand
Rational approximations for values of derivatives of the Gamma function
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 withExpand
Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae
  • T. Rivoal
  • Computer Science, Mathematics
  • Exp. Math.
  • 1 January 2004
TLDR
It is obtained that, for any integer j ≥ 0, there exists at least [j/2] + 1 Apéry-like formulae for ζ(2j + 3). Expand
ON THE BITS COUNTING FUNCTION OF REAL NUMBERS
  • T. Rivoal
  • Mathematics
  • Journal 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 numbersExpand
Remainder Pade Approximants for the Exponential Function
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, notExpand
On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps
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 seriesExpand
Rational approximation to values of G-functions, and their expansions in integer bases
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\cdotExpand
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