Communications in Number Theory and Physics
Volume 12 (2018)
Wrońskian factorizations and Broadhurst–Mellit determinant formulae
Pages: 355 – 407
Drawing on Vanhove’s contributions to mixed Hodge structures for Feynman integrals in two-dimensional 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 Broadhurst–Mellit to the logarithmic Mahler measures of certain polynomials.
Bessel moments, Feynman integrals, Wrońskian determinants, Mahler measures
2010 Mathematics Subject Classification
Primary 11R06, 15A15, 33C10, 46E25. Secondary 60G50, 81Q30, 81T18, 81T40.
This research was supported in part by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4).
Received 8 November 2017
Accepted 15 February 2018
Published 21 June 2018