On the functional equation of the Siegel series

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• 作者：Tamotsu Ikeda up>ikeda@math.kyoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding authorup>
• 关键词：11E08 ; 11E45
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：44-62
• 全文大小：333 K

文摘

It is well-known that the Fourier coefficients of Siegel–Eisenstein series can be expressed in terms of the Siegel series. The functional equation of the Siegel series of a quadratic form over ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16302104&_mathId=si1.gif&_user=111111111&_pii=S0022314X16302104&_rdoc=1&_issn=0022314X&md5=64550c722df22f4742f32dc728bc593c" title="Click to view the MathML source">Qub>pub> was first proved by Katsurada. In this paper, we prove the functional equation of the Siegel series over a non-archimedean local field of characteristic 0 by using the representation theoretic argument by Kudla and Sweet.