Series expansion of the period function and representations of Hecke operators

详细信息    查看全文

• 作者：Dohoon Choi^a ; ^{choija@kau.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Subong Lim^b ; ^{subong@skku.edu" class="auth_mail" title="E-mail the corresponding author} ; Tobias Mü ; hlenbruch^c ; ^{tobias.muehlenbruch@fernuni-hagen.de" class="auth_mail" title="E-mail the corresponding author} ; Wissam Raji^d ; ^{wr07@aub.edu.lb" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11F37 ; secondary ; 20C08 ; 32N10 ; 33B20
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：301-340
• 全文大小：576 K

文摘

The period polynomial of a cusp form of an integral weight plays an important role in the number theory. In this paper, we study the period function of a cusp form of real weight. We obtain a series expansion of the period function of a cusp form of real weight for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16302037&_mathId=si1.gif&_user=111111111&_pii=S0022314X16302037&_rdoc=1&_issn=0022314X&md5=f9d0ebaf41ba69d09651b434fad6e739" title="Click to view the MathML source">SL(2,Z)class="mathContainer hidden">class="mathCode">$\mathrm{SL}(2,\mathbb{Z})$ by using the binomial expansion. Furthermore, we study two kinds of Hecke operators acting on cusp forms and period functions, respectively. With these Hecke operators we show that there is a Hecke-equivariant isomorphism between the space of cusp forms and the space of period functions. As an application, we obtain a formula for a certain L-value of a Hecke eigenform by using the series expansion of its period function.