Calabi-Yau动机的l -导数和双扩展

Experimental Results Pub Date : 2023-07-28 DOI:10.1017/exp.2023.15

Vasily Golyshev

{"title":"Calabi-Yau动机的l -导数和双扩展","authors":"Vasily Golyshev","doi":"10.1017/exp.2023.15","DOIUrl":null,"url":null,"abstract":"Abstract We prove that certain differential operators of the form $ DLD $ with $ L $ hypergeometric and $ D=z\\frac{\\partial }{dz} $ are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the $ L $ -functions of the respective motives at $ s=2 $ .","PeriodicalId":12269,"journal":{"name":"Experimental Results","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On L-derivatives and biextensions of Calabi–Yau motives\",\"authors\":\"Vasily Golyshev\",\"doi\":\"10.1017/exp.2023.15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove that certain differential operators of the form $ DLD $ with $ L $ hypergeometric and $ D=z\\\\frac{\\\\partial }{dz} $ are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the $ L $ -functions of the respective motives at $ s=2 $ .\",\"PeriodicalId\":12269,\"journal\":{\"name\":\"Experimental Results\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Experimental Results\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/exp.2023.15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Experimental Results","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/exp.2023.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要用$ L $超几何和$ D=z\frac{\partial }{dz} $证明了形式为$ DLD $的微分算子是Picard-Fuchs型。我们给出了一类双扩展周期矩阵的子矩阵的闭超几何表达式，这些子矩阵是由假定为解析秩1的阶4权3 Calabi-Yau动机所产生的。我们将它们的值与$ s=2 $上各自动机的$ L $ -函数的一阶导数进行数值比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On L-derivatives and biextensions of Calabi–Yau motives

Abstract We prove that certain differential operators of the form $ DLD $ with $ L $ hypergeometric and $ D=z\frac{\partial }{dz} $ are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the $ L $ -functions of the respective motives at $ s=2 $ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Experimental Results

CiteScore

1.50

自引率

0.00%

发文量