Large Values of Newform Dedekind Sums

2024/05/01 by Georgia Corbett, Corbett, Georgia, Matthew P. Young +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2405.00274

Abstract

We study a generalized Dedekind sum S_χ1,χ2(a,c) attached to newform Eisenstein series E_χ1,χ2(z,s). Our work shows the Dedekind sum is rarely substantially larger than log³ c. The method of proof first relates the size of the Dedekind sum to continued fractions. A result of Hensley from 1991 then controls the average size of the maximal partial quotient in the continued fraction expansion of a/c. We complement this result by computing approximate values of the Dedekind sum in some special cases, which in particular produces examples of large values of the Dedekind sum.

Cited by

• Higher Weight Generalized Dedekind Sums

Related

• The largest values of Dedekind sums
• Algebraic properties of the values of newform Dedekind sums
• Higher Weight Generalized Dedekind Sums
• Mean values of Dedekind sums
• Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions