Results 1 to 10 of about 1,466 (25)
Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
Advances in Difference Equations, 2021 The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group.
Yuankui Ma +4 more
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Identities on poly-Dedekind sums
Advances in Difference Equations, 2020 Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums.
Taekyun Kim +3 more
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Generalized Dedekind eta-functions and generalized Dedekind sums [PDF]
Transactions of the American Mathematical Society, 1973 A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.
openaire +2 more sources
Elementary proofs of Berndt's reciprocity laws [PDF]
, 1982 Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmetical sums analogous to Dedekind sums. This paper gives elementary proofs of all three reciprocity laws and obtains them all from a common source, a ...
Apostol, Tom M., Vu, Thiennu H.
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On cubic multisections of Eisenstein series [PDF]
, 2013 A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three.
Alaniz, Andrew, Huber, Tim
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series [PDF]
, 2007 We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademacher sums arise. In the course of its proof, we also obtain a transformation formula for elliptic Dedekind-Rademacher sums. When a complex parameter $¥tau$
Machide, Tomoya
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Quantum Invariant, Modular Form, and Lattice Points [PDF]
, 2004 We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold with 4-singular fibers. We define the Eichler integrals of the modular forms with half-integral weight, and we show that the invariant is rewritten as a sum of the Eichler ...
Hikami, Kazuhiro
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Records on the vanishing of Fourier coefficients of Powers Of the Dedekind Eta Function
, 2018 In this paper we significantly extend Serre's table on the vanishing properties of Fourier coefficients of odd powers of the Dedekind eta function. We address several conjectures of Cohen and Str\"omberg and give a partial answer to a question of Ono. In
Heim, Bernhard +2 more
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On the distribution of Dedekind sums [PDF]
, 2017 Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums.
Girstmair, Kurt
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