Wrońskian因式分解和Broadhurst-Mellit行列式公式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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