Transformation laws for generalized Dedekind sums associated to Fuchsian groups

Claire Burrin, Jay Jorgenson, Cormac O’Sullivan, Lejla Smajlović Acta Arithmetica MSC: 11F20, 30F35. DOI: 10.4064/aa190425-31-1 Opublikowany online: 19 June 2020

Streszczenie

We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups $\Gamma _0(N)$, and the non-congruence arithmetic groups $\Gamma _0(N)^+$.

Autorzy

  • Claire BurrinDepartment of Mathematics
    Rutgers University
    Piscataway, NJ 08854, U.S.A.
    e-mail
  • Jay JorgensonDepartment of Mathematics
    The City College of New York
    New York, NY 10031, U.S.A.
    e-mail
  • Cormac O’SullivanDepartment of Mathematics
    The CUNY Graduate Center
    New York, NY 10016, U.S.A.
    e-mail
  • Lejla SmajlovićDepartment of Mathematics
    University of Sarajevo
    71000 Sarajevo, Bosnia and Herzegovina
    e-mail

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