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 Mahler measures of certain polynomials.

中文翻译：

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Wrońskian 分解和 Broadhurst-Mellit 行列式公式

利用 Vanhove 对二维量子场论中费曼积分的混合霍奇结构的贡献，我们计算了两个行列式，其条目是贝塞尔矩。通过对某些 Wronskian 行列式进行显式分解，我们验证了 Broadhurst 和 Mellit 提出的两个最近关于任意大小行列式的猜想。通过对我们的方法的一些扩展，我们还将 Broadhurst 的另外两个决定因素——梅利特与某些多项式的对数马勒测度联系起来。