Wrońskian factorizations and Broadhurst–Mellit determinant formulae

@article{Zhou2017WroskianFA,
  title={Wrońskian factorizations and Broadhurst–Mellit determinant formulae},
  author={Yajun Zhou},
  journal={Communications in Number Theory and Physics},
  year={2017},
  volume={12},
  pages={355-407}
}
  • Yajun Zhou
  • Published 6 November 2017
  • Mathematics
  • Communications in Number Theory and Physics
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 Wronskian 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… 
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Through algebraic manipulations on Wronskian matrices whose entries are reducible to Bessel moments, we present a new analytic proof of the quadratic relations conjectured by Broadhurst and Roberts,
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