{"title":"Wrońskian因式分解和Broadhurst-Mellit行列式公式","authors":"Yajun Zhou","doi":"10.4310/CNTP.2018.v12.n2.a5","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"12 1","pages":"355-407"},"PeriodicalIF":1.2000,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Wrońskian factorizations and Broadhurst–Mellit determinant formulae\",\"authors\":\"Yajun Zhou\",\"doi\":\"10.4310/CNTP.2018.v12.n2.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":55616,\"journal\":{\"name\":\"Communications in Number Theory and Physics\",\"volume\":\"12 1\",\"pages\":\"355-407\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2017-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Number Theory and Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/CNTP.2018.v12.n2.a5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Number Theory and Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/CNTP.2018.v12.n2.a5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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