Generalized Dedekind Eta-Functions and Generalized Dedekind Sums

DOI10.2307/1996714zbMath0262.10015OpenAlexW4254561014MaRDI QIDQ5677556

Bruce C. Berndt

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/1996714

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

Relations between theta-functions, Hardy sums, Eisenstein and Lambert series in the transformation formula of log \(\eta_{g,h}(z)\). ⋮ Ramanujan’s Formula for ζ(2n + 1) ⋮ SOME INFINITE SERIES IDENTITIES ⋮ \(q\)-Dedekind type sums related to \(q\)-zeta function and basic \(L\)-series ⋮ Several new product identities in relation to Rogers-Ramanujan type sums and mock theta functions ⋮ On generalized Eisenstein series and Ramanujan's formula for periodic zeta-functions ⋮ Applications of the theory of modular forms to number theory ⋮ Generalized eta-functions and certain ray class invariants of real quadratic fields ⋮ Elementary proof of the transformation formula for Lambert series involving generalized Dedekind sums ⋮ Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas ⋮ Quotients of values of the Dedekind eta function ⋮ On series identities arising from Jacobi’s identity of the theta function ⋮ Periodic analogues of Dedekind sums and transformation formulas of Eisenstein series ⋮ On Dirichlet \(L\)-functions with periodic coefficients and Eisenstein series ⋮ Reciprocity theorems for Dedekind sums and generalizations ⋮ Ramanujan type formulas for \(\zeta (2k-1)\) ⋮ Rationality of secant zeta values ⋮ On multiple analogues of Ramanujan's formulas for certain Dirichlet series ⋮ Higher-order character Dedekind sum ⋮ Generalized Eisenstein series and several modular transformation formulae ⋮ Some new reciprocity formulas for generalized Dedekind sums

Cites Work

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