Dedekind sums arising from newform Eisenstein series
Abstract
For primitive nontrivial Dirichlet characters [Formula: see text] and [Formula: see text], we study the weight zero newform Eisenstein series [Formula: see text] at [Formula: see text]. The holomorphic part of this function has a transformation rule that we express in finite terms as a generalized Dedekind sum. This gives rise to the explicit construction (in finite terms) of elements of [Formula: see text]. We also give a short proof of the reciprocity formula for this Dedekind sum.
Faculty Members
- M. P. Young - Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
- T. Stucker - University of Idaho, Moscow, ID 83844, USA
- A. Vennos - Salisbury University, Salisbury, MD 21801, USA
Themes
- Dedekind sums
- Dirichlet characters
- reciprocity formula
- Eisenstein series
- transformation rules