Hilbert Transforms and Sum Rules of Bessel Moments
Classical Analysis and ODEs
2019-01-23 v2 High Energy Physics - Theory
Number Theory
Abstract
Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we verify and generalize two conjectures by Bailey-Borwein-Broadhurst-Glasser and Broadhurst-Mellit.
Cite
@article{arxiv.1706.01068,
title = {Hilbert Transforms and Sum Rules of Bessel Moments},
author = {Yajun Zhou},
journal= {arXiv preprint arXiv:1706.01068},
year = {2019}
}
Comments
(v1) 9 pages. Verification and generalization of the integrality for Crandall numbers (OEIS A262961) (v2) 10 pages. Minor corrections and additions. Revised according to referee's report