Dedekind sums arising from newform Eisenstein series-Reference-Cited by-同舟云学术

Dedekind sums arising from newform Eisenstein series

Published:2020-08-21 Issue:10 Volume:16 Page:2129-2139
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Stucker T.¹,Vennos A.²,Young M. P.³

Affiliation:

1. University of Idaho, Moscow, ID 83844, USA

2. Salisbury University, Salisbury, MD 21801, USA

3. Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

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.

Funder

the National Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120501092

Reference15 articles.

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2. B. Berndt, Character Transformation Formulae Similar to Those for The Dedekind Eta-Function, Proceedings of Symposia in Pure Mathematics, Vol. 24 (American Mathematical Society, Providence, RI, 1973), pp. 9–30.

3. On Eisenstein series with characters and the values of Dirichlet L-functions

4. Character analogues of the poisson and Euler-MacLaurin summation formulas with applications

5. Degenerate and character Dedekind sums

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