Wro\'nskian factorizations and Broadhurst-Mellit determinant formulae
Yajun Zhou
TL;DR
This paper verifies conjectures about determinants of Bessel moments related to Feynman integrals using Wronskian factorizations, and connects some determinants to Mahler measures, advancing understanding in mathematical physics.
Contribution
It introduces explicit Wronskian factorizations to prove Broadhurst and Mellit's conjectures on determinants of Bessel moments and relates these determinants to Mahler measures.
Findings
Verified two conjectures on determinants of Bessel moments.
Established explicit factorizations of Wronskian determinants.
Connected certain determinants to Mahler measures of polynomials.
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.
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