Wro\'nskian factorizations and Broadhurst-Mellit determinant formulae
Classical Analysis and ODEs
2018-06-25 v2 High Energy Physics - Theory
Number Theory
Abstract
Drawing on Vanhove's contributions to mixed Hodge structures for Feynman integrals in two-di\-men\-sion\-al quantum field theory, we compute two families of determinants whose entries are Bessel moments. Via explicit factorizations of certain Wro\'nskian determinants, we verify two recent conjectures proposed by Broadhurst and Mellit, concerning determinants of arbitrary sizes. With some extensions to our methods, we also relate two more determinants of Broadhurst--Mellit to the logarithmic Mahler measures of certain polynomials.
Keywords
Cite
@article{arxiv.1711.01829,
title = {Wro\'nskian factorizations and Broadhurst-Mellit determinant formulae},
author = {Yajun Zhou},
journal= {arXiv preprint arXiv:1711.01829},
year = {2018}
}
Comments
i+32 pages. Proof of two conjectures proposed by Broadhurst-Mellit (arXiv:1604.03057), using Vanhove's theory (arXiv:1401.6438). Evaluation of vacuum determinants via Mahler measures, in a new Section 5