椭圆型Dedekind和的密度

IF 0.5 3区数学 Q3 MATHEMATICS

Acta Arithmetica Pub Date : 2022-08-05 DOI:10.4064/aa210921-27-7

Nicolas Berkopec, Jacob Branch, Rachel Heikkinen, C. Nunn, T. Wong

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引用次数: 0

摘要

椭圆型Dedekind和是由R. schzech作为经典Dedekind和在复格上的推广引入的。我们证明了对于任意具有实数$j$不变量的格，适当归一化椭圆Dedekind和的值在实数上是稠密的。这推广了伊藤关于欧几里德虚二次环的一个早期结果。我们的证明改编了Kohnen最近的工作，该工作给出了经典Dedekind和值密度的新证明。

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The density of elliptic Dedekind sums

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. Our proof is an adaptation of the recent work of Kohnen, which gives a new proof of the density of values of classical Dedekind sums.

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