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Rational period functions and indefinite binary quadratic forms in higher level cases

Volume 179 / 2017

SoYoung Choi, Chang Heon Kim Acta Arithmetica 179 (2017), 319-334 MSC: Primary 11F11; Secondary 11F67. DOI: 10.4064/aa8556-2-2017 Published online: 1 August 2017

Abstract

Generalizing Gethner’s 1993 result we prove that rational period functions with irrational poles in higher level cases are not Hecke eigenfunctions. We also provide examples of rational period functions in level $2$ with irrational poles associated with indefinite binary quadratic forms by extending Choie and Parson’s 1990 result.

Authors

  • SoYoung ChoiDepartment of Mathematics Education and RINS
    Gyeongsang National University
    501 Jinjudae-ro, Jinju, 660-701, South Korea
    e-mail
  • Chang Heon KimDepartment of Mathematics
    Sungkyunkwan University
    Suwon, 440-746, South Korea
    e-mail

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