Dedekind and Hardy sums
Dedekind cotangent sums
Dedekind sums and continued fractions
Dedekind sums and signatures of intersection forms.
Dedekind sums for Hecke groups
Dedekind sums, ..-invariants and the signature cocycle.
Dedekind sums involving Jacobi modular forms and special values of Barnes zeta functions
In this paper we study three new shifted sums of Apostol-Dedekind-Rademacher type. The first sums are written in terms of Jacobi modular forms, and the second sums in terms of cotangent and the third sums are expressed in terms of special values of the Barnes multiple zeta functions. These sums generalize the classical Dedekind-Rademacher sums. The main aim of this paper is to state and prove the Dedekind reciprocity laws satisfied by these new sums. As an application of our Dedekind reciprocity...
Dedekind sums with characters and class numbers of imaginary quadratic fields
Dedekind sums with predictable signs
Dedekind type sums and Hecke operators
Dedekind-Rademacher sums and their reciprocity formula.
Ein einfacher Beweis der Transformationsformel für log ... (z).
Eisenstein cocycles for GL2Q and values of L-function in real quadratic fields.
Elliptic units of cyclic unramified extensions of complex quadratic fields
Equality of Dedekind sums modulo 8ℤ
Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Explicit evaluations of the Rogers-Ramanujan continued fraction.
Fourth power mean of character sums
Generalizations of Dedekind sums and their reciprocity laws
Generalized Dedekind sums.