#### 10 Citations

Arithmetic of linear forms involving odd zeta values

- Mathematics
- 2002

The story exposed in this paper starts in 1978, when R. Apery [Ap] gave a surprising sequence of exercises demonstrating the irrationality of ζ(2) and ζ(3). (For a nice explanation of Apery’s… Expand

Approximation Measures for Logarithms of Algebraic Numbers FRANCESCO AMOROSO-CARLO

- 2019

Given a number field K and a number ) lll we say that A > 0 is a K-irrationality measure of 03BE if, for any e > 0, > ( 1 + e) p h(o) for all p E K with sufficiently large Weil logarithmic height… Expand

HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS

- Mathematics
- Kyushu Journal of Mathematics
- 2019

We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying `permutation group'… Expand

Multiple Legendre polynomials in diophantine approximation

- Mathematics
- 2014

We construct a class of multiple Legendre polynomials and prove that they satisfy an Apery-like recurrence. We give new upper bounds of the approximation measures of logarithms of rational numbers by… Expand

IRRATIONALITY AND NONQUADRATICITY MEASURES FOR LOGARITHMS OF ALGEBRAIC NUMBERS

- Mathematics
- Journal of the Australian Mathematical Society
- 2012

Abstract Let 𝕂⊂ℂ be a number field. We show how to compute 𝕂-irrationality measures of a number ξ∉𝕂, and 𝕂-nonquadraticity measures of ξ if [𝕂(ξ):𝕂]>2. By applying the saddle point method to a… Expand

A refinement of Nesterenko’s linear independence criterion with applications to zeta values

- Mathematics
- 2010

We refine (and give a new proof of) Nesterenko’s famous linear independence criterion from 1985, by making use of the fact that some coefficients of linear forms may have large common divisors. This… Expand

NEW IRRATIONALITY RESULTS FOR DILOGARITHMS OF RATIONAL NUMBERS

- Mathematics
- 2008

A natural method to investigate diophantine properties of transcendental (or conjecturally transcendental) constants occurring in various mathematical contexts consists in the search for sequences of… Expand

Linear independence of linear forms in polylogarithms

- Mathematics
- 2006

For x ∈ C, |x | < 1, s ∈ N, let Lis(x) be the s-th polylogarithm of x . We prove that for any non-zero algebraic number α such that |α| < 1, the Q(α)-vector space spanned by 1, Li1(α), Li2(α), . . .… Expand

An essay on irrationality measures of pi and other logarithms

- Mathematics
- 2004

We present a brief survey of the methods used in deducing upper estimates for irrationality measures of the logarithm values. We particularly expose the best known estimates for $\log2$ (due to E.… Expand

Irrationality Measures of log 2 and π/√3

- Mathematics, Computer Science
- Exp. Math.
- 2001

Using a class of polynomials that generalizes Legendre polynmials, this work unify previous works of E. V. Chudnovsky about irrationality measures of log 2 and π/√3. Expand