Series expansion of the period function and representations of Hecke operators

JOURNAL OF NUMBER THEORY

卷:171

Article

Choi, Dohoon¹  Lim, Subong²  Muehlenbruch, Tobias³  Raji, Wissam⁴ 

[1] Korea Aerosp Univ, Sch Liberal Arts & Sci, 200-1 Hwajeon Dong, Goyang 412791, Gyeonggi, South Korea

[2] Sungkyunkwan Univ, Dept Math Educ, 25-2 Sungkyunkwan Ro, Seoul 03063, South Korea

[3] Fernuniv, Dept Math & Comp Sci, D-58084 Hagen, Germany

[4] Amer Univ Beirut, Dept Math, Beirut, Lebanon

关键词: Period functions;    Eichler-Shimura cohomology;    Hecke operators;   

DOI  :  10.1016/j.jnt.2016.07.020

来源: Elsevier

【 摘 要 】

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 SL(2,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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free