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The density of elliptic Dedekind sums

Volume 205 / 2022

Nicolas Berkopec, Jacob Branch, Rachel Heikkinen, Caroline Nunn, Tian An Wong Acta Arithmetica 205 (2022), 33-40 MSC: Primary 11F20; Secondary 11A15. DOI: 10.4064/aa210921-27-7 Published online: 19 September 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. 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.


  • Nicolas BerkopecUniversity of New Mexico
    3308 Mountain Rd. NE
    Albuquerque, NM 87106, USA
  • Jacob BranchFairmont State University
    9 Hutchinson Drive
    Fairmont, WV 26554, USA
  • Rachel HeikkinenAugustana College
    Olin Center 820 38th St
    Rock Island, IL 61201, USA
  • Caroline NunnUniversity of Wisconsin-Madison
    Van Vleck Hall
    480 Lincoln Drive
    Madison, WI 53706, USA
  • Tian An WongUniversity of Michigan-Dearborn
    4901 Evergreen Rd
    2002 CASL Building
    Dearborn, MI 48128, USA

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