{"title":"SO+(2,n + 2) 的赫克理论","authors":"Aloys Krieg , Hannah Römer , Felix Schaps","doi":"10.1016/j.jnt.2024.03.003","DOIUrl":null,"url":null,"abstract":"<div><p>We describe the foundations of a Hecke theory for the orthogonal group <span><math><mi>S</mi><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></span>. In particular we consider the Hermitian modular group of degree 2 as a special example of <span><math><mi>S</mi><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span>. As an application we show that the attached Maaß space is invariant under Hecke operators. This implies that the Eisenstein series belongs to the Maaß space. If the underlying lattice is even and unimodular, our approach allows us to reprove the explicit formula of its Fourier coefficients.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022314X24000805/pdfft?md5=f514dbc566b927d06d054aab5bbe88a7&pid=1-s2.0-S0022314X24000805-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Hecke theory for SO+(2,n + 2)\",\"authors\":\"Aloys Krieg , Hannah Römer , Felix Schaps\",\"doi\":\"10.1016/j.jnt.2024.03.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We describe the foundations of a Hecke theory for the orthogonal group <span><math><mi>S</mi><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></span>. In particular we consider the Hermitian modular group of degree 2 as a special example of <span><math><mi>S</mi><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span>. As an application we show that the attached Maaß space is invariant under Hecke operators. This implies that the Eisenstein series belongs to the Maaß space. If the underlying lattice is even and unimodular, our approach allows us to reprove the explicit formula of its Fourier coefficients.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24000805/pdfft?md5=f514dbc566b927d06d054aab5bbe88a7&pid=1-s2.0-S0022314X24000805-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24000805\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24000805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We describe the foundations of a Hecke theory for the orthogonal group . In particular we consider the Hermitian modular group of degree 2 as a special example of . As an application we show that the attached Maaß space is invariant under Hecke operators. This implies that the Eisenstein series belongs to the Maaß space. If the underlying lattice is even and unimodular, our approach allows us to reprove the explicit formula of its Fourier coefficients.
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