Modular forms, generalized Dedekind symbols and period polynomials

DOI10.1007/s002080050138zbMath0886.11025OpenAlexW2051353259MaRDI QIDQ1377074

Shinji Fukuhara

Publication date: 1 February 1998

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050138

zbMATH Keywords

Dedekind sumsreciprocity lawmodular formsspace of cusp formsperiod polynomialsgeneralized Dedekind symbolshomogeneous Laurent polynomial

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20)

Related Items (18)

A few finite trigonometric sums ⋮ Equidistribution of generalized Dedekind sums and exponential sums ⋮ Elliptic Apostol sums and their reciprocity laws ⋮ New trigonometric identities and generalized Dedekind sums ⋮ Holomorphic Automorphic Forms and Cohomology ⋮ Dedekind symbols with plus reciprocity laws ⋮ Twisted Hecke \(L\)-values and period polynomials ⋮ Generating functions of even Dedekind symbols with polynomial reciprocity laws ⋮ Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials ⋮ A generating function of higher-dimensional Apostol--Zagier sums and its reciprocity law ⋮ The elliptic Apostol-Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws ⋮ Explicit formulae for two-bridge knot polynomials ⋮ Hecke operators on weighted Dedekind symbols ⋮ Quantum modular forms and Hecke operators ⋮ Modular forms of real weights and generalised Dedekind symbols ⋮ Twisted generalized Dedekind symbols ⋮ Explicit evaluations and reciprocity theorems for finite trigonometric sums ⋮ Dedekind symbols associated with J-forms and their reciprocity law.

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