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The density of elliptic Dedekind sums
Acta Arithmetica, 2022 Elliptic Dedekind sums were introduced by R. Sczech as generalizations of classical Dedekind sums to complex lattices. We show that for any lattice with real $j$-invariant, the values of suitably normalized elliptic Dedekind sums are dense in the real numbers. This extends an earlier result of Ito for Euclidean imaginary quadratic rings.
Berkopec, Nicolas +4 more
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Reciprocity and the kernel of Dedekind sums
Research in Number Theory, 2023 9 pages, 2 ...
Alexis LaBelle +2 more
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Fractional parts of Dedekind sums [PDF]
, 2015 Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec~(1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums $s(m,n)$
Banks, William D., Shparlinski, Igor E.
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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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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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On Restricted Averages of Dedekind Sums
International Mathematics Research Notices, 2023 Abstract We investigate the averages of Dedekind sums over rational numbers in the set $\mathscr {F}_{\alpha }(Q) = \{\,{v}/{w}\in \mathbb {Q}: 0<w\leq Q\,\}\cap \lbrack 0, \alpha )$ for fixed $\alpha \leq 1/2$. In previous work, we obtained asymptotics for $\alpha =1/2$, confirming a conjecture of Ito in a quantitative form.
Minelli, Paolo +2 more
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The reciprocity theorem for Dedekind sums [PDF]
Pacific Journal of Mathematics, 1953 Let \(((x)) = x - [x] - \tfrac12\) where \([x]\) denotes the integral part of \(x\). Define the Dedekind sum \(S(h, k)\) by \[ S(h, k) = \sum_{r\pmod k} \left(\left(\frac{r}{k}\right)\right) \left(\left(\frac{rh}{k}\right)\right). \] Dedekind and later various authors proved the reciprocity formula \[ 12hk (S(h, k) + S(k, h)) = h^2 + 3kh + k^2 + 1 \tag{
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On Lehmer’s problem and Dedekind sums [PDF]
Czechoslovak Mathematical Journal, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pan, Xiaowei, Zhang, Wenpeng
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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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