Rational period functions in higher level cases

JOURNAL OF NUMBER THEORY

卷:157

Article

Choi, So Young¹  Kim, Chang Heon² 

[1] Dongguk Univ Gyeongju, Dept Math Educ, Gyeongju 780714, South Korea

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

关键词: Period functions;    Modular integrals;    Hecke operators;   

DOI  :  10.1016/j.jnt.2015.04.021

来源: Elsevier

【 摘 要 】

Extending Knopp's results [9,10] we investigate examples and properties of rational period functions in higher level cases, including location of poles and behavior under the action of Hecke operators. More precisely, we prove that a rational period function may have poles only at 0 or at real quadratic irrationalities. Moreover by applying the action of Hecke operators we prove that for positive odd integer k and p is an element of {2, 3}, the space of all rational period functions of weight 2k for r(0)(+)(p) is infinite dimensional. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free