Zeros of the dilogarithm
Number Theory
2015-07-30 v1 Classical Analysis and ODEs
Abstract
We show that the dilogarithm has at most one zero on each branch, that each zero is close to a root of unity, and that they may be found to any precision with Newton's method. This work is motivated by applications to the asymptotics of coefficients in partial fraction decompositions considered by Rademacher. We also survey what is known about zeros of polylogarithms in general.
Keywords
Cite
@article{arxiv.1507.07980,
title = {Zeros of the dilogarithm},
author = {Cormac O'Sullivan},
journal= {arXiv preprint arXiv:1507.07980},
year = {2015}
}
Comments
24 pages