Linear independence of dilogarithmic values

  title={Linear independence of dilogarithmic values},
  author={Carlo Viola and Wadim Zudilin},
  journal={Crelle's Journal},
Linear Forms in Polylogarithms
Let $r, \,m$ be positive integers. Let $x$ be a rational number with $0 \le x <1$. Consider $\Phi_s(x,z) =\displaystyle\sum_{k=0}^{\infty}\frac{z^{k+1}}{{(k+x+1)}^s}$ the $s$-th Lerch function withExpand
Vectors of type II Hermite–Padé approximations and a new linear independence criterion
We propose a linear independence criterion, and outline an application of it. Down to its simplest case, it aims at solving this problem: given three real numbers, typically as special values ofExpand
Can polylogarithms at algebraic points be linearly independent?
Let $r,m$ be positive integers. Let $0\le x <1$ be a rational number. Let $\Phi_s(x,z)$ be the $s$-th Lerch function $\sum_{k=0}^{\infty}\tfrac{z^{k+1}}{(k+x+1)^s}$ with $s=1,2,\ldots ,r$. WhenExpand


Multiple Legendre polynomials in diophantine approximation
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 byExpand
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best pre- viously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying ourExpand
Rational approximations to the dilogarithm
The irrationality proof of the values of the dilogarithmic function L 2 (z) at rational points z = 1/k for every integer k ∈ (−∞, −5] ∪ [7, ∞) is given. To show this we develop the method ofExpand
An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities
SummaryIt is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructibleExpand
The Irrationality of √2