AbstractSums of Dedekind type are defined by the formula f(h, k) = Σμ(mod k) A(μk) B(hμk), where each of A(x) and B(x) satisfies a multiplication formula of the form Σb(mod q) F(x + bq) = qν(F) F(qx). Properties of these sums are obtained, including an extension of M. I. Knopp's identity for the classical Dedekind sums s(h, k)
1. Background. Dedekind sums are classical objects of study intro-duced by Richard Dedekind in the 1...
We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademac...
AbstractA necessary and sufficient condition is given for a positive integer to appear as the denomi...
AbstractSums of Dedekind type are defined by the formula f(h, k) = Σμ(mod k) A(μk) B(hμk), where eac...
AbstractIf h, k ∈ Z, k > 0, the Dedekind sum is given by s(h,k) = ∑μ=1kμkhμk, with ((x)) = x − [x] −...
AbstractA brief and elementary proof of Petersson and Knopp's recent theorem on Dedekind sums is giv...
In this paper, we express three different, yet related, character sums in terms of generalized Berno...
AbstractGeneralized reciprocity formulas and Dedekind-Petersson-Knopp-type formulas are given to gen...
In this paper, for any multivariable function with a periodicity and a certain distribution relation...
AbstractA simple proof of the identity D(a, c) = − D(a, c) for the Dedekind sums D(a, c) introduced ...
AbstractIn this paper we give a simple proof for the reciprocity formula for the generalized Dedekin...
summary:The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many a...
AbstractFor integers a, b and n > 0 we define SΓ(a,b,n) = ∑r=0n∤brn−1arn ln Γbrn andSΓ(a,b,n) = ∑r=0...
AbstractAn elementary proof is given of the author's transformation formula for the Lambert series G...
For integers a, b and n > 0 we define [GRAPHICS] and [GRAPHICS] which are similar to the homogeneous...
1. Background. Dedekind sums are classical objects of study intro-duced by Richard Dedekind in the 1...
We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademac...
AbstractA necessary and sufficient condition is given for a positive integer to appear as the denomi...
AbstractSums of Dedekind type are defined by the formula f(h, k) = Σμ(mod k) A(μk) B(hμk), where eac...
AbstractIf h, k ∈ Z, k > 0, the Dedekind sum is given by s(h,k) = ∑μ=1kμkhμk, with ((x)) = x − [x] −...
AbstractA brief and elementary proof of Petersson and Knopp's recent theorem on Dedekind sums is giv...
In this paper, we express three different, yet related, character sums in terms of generalized Berno...
AbstractGeneralized reciprocity formulas and Dedekind-Petersson-Knopp-type formulas are given to gen...
In this paper, for any multivariable function with a periodicity and a certain distribution relation...
AbstractA simple proof of the identity D(a, c) = − D(a, c) for the Dedekind sums D(a, c) introduced ...
AbstractIn this paper we give a simple proof for the reciprocity formula for the generalized Dedekin...
summary:The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many a...
AbstractFor integers a, b and n > 0 we define SΓ(a,b,n) = ∑r=0n∤brn−1arn ln Γbrn andSΓ(a,b,n) = ∑r=0...
AbstractAn elementary proof is given of the author's transformation formula for the Lambert series G...
For integers a, b and n > 0 we define [GRAPHICS] and [GRAPHICS] which are similar to the homogeneous...
1. Background. Dedekind sums are classical objects of study intro-duced by Richard Dedekind in the 1...
We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademac...
AbstractA necessary and sufficient condition is given for a positive integer to appear as the denomi...
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