论文标题
椭圆形的密度总和
The Density of Elliptic Dedekind Sums
论文作者
论文摘要
R. Sczech将椭圆形的Dedekind总和作为对复杂晶格的经典Dedekind总和的概括。我们表明，对于任何带有真正$ j $ invariant的晶格，适当正常化的椭圆形的dedekind总和的值在实数中是密集的。这扩展了欧几里得假想二次环的ITO的较早结果。我们的证明是对Kohnen最近工作的改编，该工作提供了新的经典Dedekind总和价值密度的新证明。
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.
