2016/08/09 by Sauvaget, Thomas
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1608.03174
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.