Hecke operators on weighted Dedekind symbols

Details Hecke operators on weighted Dedekind symbols Hecke operators on weighted Dedekind symbols

2004-12-05

arxiv.org/abs/math/0412090v1

Mathematics

Number Theory

AMS-LaTeX, 24 pages

Scientific paper

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with polynomial (Laurent polynomial) reciprocity laws and the space of cusp (modular) forms. In this article we introduce Hecke operators on the space of weighted Dedekind symbols. We prove that these newly introduced operators are compatible with Hecke operators on the space of modular forms. As an application, we present formulae to give Fourier coefficients of Hecke eigenforms. In particular we give explicit formulae for generalized Ramanujan's tau functions.

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