的阿基米德zeta积分𝐺𝐿（3） ×𝐺𝐿（2）

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2022-07-01 DOI:10.1090/memo/1366

Miki Hirano, Taku Ishii, Tadashi Miyazaki

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Moreover, we apply those to the calculation of archimedean zeta integrals for <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G upper L left-parenthesis 3 right-parenthesis times upper G upper L left-parenthesis 2 right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>G</mml:mi>\n <mml:mi>L</mml:mi>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>3</mml:mn>\n <mml:mo stretchy=\"false\">)</mml:mo>\n <mml:mo>×</mml:mo>\n <mml:mi>G</mml:mi>\n <mml:mi>L</mml:mi>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>2</mml:mn>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">GL(3)\\times GL(2)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>, and show that the zeta integral for appropriate Whittaker functions is equal to the associated <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\n <mml:semantics>\n <mml:mi>L</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-factors.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2)\",\"authors\":\"Miki Hirano, Taku Ishii, Tadashi Miyazaki\",\"doi\":\"10.1090/memo/1366\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we give explicit formulas of archimedean Whittaker functions on <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper G upper L left-parenthesis 3 right-parenthesis\\\">\\n <mml:semantics>\\n <mml:mrow>\\n <mml:mi>G</mml:mi>\\n <mml:mi>L</mml:mi>\\n <mml:mo stretchy=\\\"false\\\">(</mml:mo>\\n <mml:mn>3</mml:mn>\\n <mml:mo stretchy=\\\"false\\\">)</mml:mo>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">GL(3)</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> and <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper G upper L left-parenthesis 2 right-parenthesis\\\">\\n <mml:semantics>\\n <mml:mrow>\\n <mml:mi>G</mml:mi>\\n <mml:mi>L</mml:mi>\\n <mml:mo stretchy=\\\"false\\\">(</mml:mo>\\n <mml:mn>2</mml:mn>\\n <mml:mo stretchy=\\\"false\\\">)</mml:mo>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">GL(2)</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>. 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引用次数: 1

摘要

本文给出了GL(3) GL(3)和GL(2) GL(2)上的阿基米德惠特克函数的显式公式。此外，我们将这些应用于GL(3) × GL(2) GL(3)\乘以GL(2)的阿基米德zeta积分的计算，并证明了适当的Whittaker函数的zeta积分等于相关的L -因子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2)

In this article, we give explicit formulas of archimedean Whittaker functions on G L ( 3 ) GL(3) and G L ( 2 ) GL(2) . Moreover, we apply those to the calculation of archimedean zeta integrals for G L ( 3 ) × G L ( 2 ) GL(3)\times GL(2) , and show that the zeta integral for appropriate Whittaker functions is equal to the associated L L -factors.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464