arXiv subjects
Publications and source records attributed to Thomas Sauvaget.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
Using a polylogarithmic identity, we express the values of $ζ$ at odd integers $2n+1$ as integrals over unit $n-$dimensional hypercubes of simple functions involving products of logarithms. We also prove a useful property of those functions as some of their variables are raised to a power. In the case $n=2$, we prove two closed-form expressions concerning related integrals. Finally, another family of related one-dimensional integrals is studied.
An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.