English

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.

Keywords

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