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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… Expand

On the integrality of the Taylor coefficients of mirror maps

- C. Krattenthaler, T. Rivoal
- Mathematics, Physics
- 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… Expand

Irrationality measures for some automatic real numbers

- B. Adamczewski, T. Rivoal
- Mathematics
- Mathematical 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… Expand

Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps

- C. Krattenthaler, T. Rivoal
- Mathematics, Physics
- 18 April 2008

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 of… Expand

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… Expand

Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae

- T. Rivoal
- Computer Science, Mathematics
- Exp. Math.
- 1 January 2004

TLDR

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 numbers… Expand

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… Expand

On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps

- É. 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… Expand

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… Expand

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