New trigonometric identities and generalized Dedekind sums

DOI10.3836/tjm/1244208679zbMath1048.11036OpenAlexW2059647931MaRDI QIDQ1429180

Shinji Fukuhara

Publication date: 18 May 2004

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1244208679

zbMATH Keywords

Hurwitz zeta functionDedekind sumtrigonometric identity

Mathematics Subject Classification ID

Dedekind eta function, Dedekind sums (11F20) Trigonometric and exponential sums (general theory) (11L03) Hurwitz and Lerch zeta functions (11M35)

Related Items (6)

Elliptic Apostol sums and their reciprocity laws ⋮ Human and automated approaches for finite trigonometric sums ⋮ Exact evaluations and reciprocity theorems for finite trigonometric sums ⋮ Reciprocal relations for trigonometric sums ⋮ General order Euler sums with multiple argument ⋮ Explicit evaluations and reciprocity theorems for finite trigonometric sums

Cites Work

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• Cotangent sums, a further generlization of Dedekind sums
• Reciprocity theorems for Dedekind sums and generalizations
• Modular forms, generalized Dedekind symbols and period polynomials
• Dedekind symbols associated with J-forms and their reciprocity law.
• Higher dimensional Dedekind sums
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Theorems on generalized Dedekind sums
• The index of elliptic operators over V-manifolds
• \(W\)-invariants and Neumann-Siebenmann invariants for Seifert homology 3-spheres

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