Wrońskian因式分解和Broadhurst-Mellit行列式公式

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2017-11-06 DOI:10.4310/CNTP.2018.v12.n2.a5

Yajun Zhou

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引用次数: 20

摘要

利用Vanhove对Feynman积分的混合Hodge结构的贡献，我们计算了两个以贝塞尔矩为元素的行列式族。通过对某些朗斯基行列式的显式分解，我们验证了Broadhurst和Mellit最近提出的关于任意大小行列式的两个猜想。通过对我们方法的一些扩展，我们还将Broadhurst- Mellit的另外两个行列式与某些多项式的对数马勒测度联系起来。

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Wrońskian factorizations and Broadhurst–Mellit determinant formulae

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.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.