Wrońskian factorizations and BroadhurstMellit determinant formulae
Abstract
Drawing on Vanhove's contributions to mixed Hodge structures for Feynman integrals in twodi\men\sion\al quantum field theory, we compute two families of determinants whose entries are Bessel moments. Via explicit factorizations of certain Wrońskian 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 BroadhurstMellit to the logarithmic Mahler measures of certain polynomials.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.01829
 Bibcode:
 2017arXiv171101829Z
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 High Energy Physics  Theory;
 Mathematics  Number Theory;
 33C10;
 46E25;
 15A15;
 11R06 (Primary) 81T18;
 81T40;
 81Q30;
 60G50 (Secondary)
 EPrint:
 i+32 pages. Proof of two conjectures proposed by BroadhurstMellit (arXiv:1604.03057), using Vanhove's theory (arXiv:1401.6438). Evaluation of vacuum determinants via Mahler measures, in a new Section 5