Large Values of Newform Dedekind Sums
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911861153202176 |
|---|---|
| author | Corbett, Georgia Young, Matthew P. |
| author_facet | Corbett, Georgia Young, Matthew P. |
| contents | We study a generalized Dedekind sum $S_{χ_1,χ_2}(a,c)$ attached to newform Eisenstein series $E_{χ_1,χ_2}(z,s)$. Our work shows the Dedekind sum is rarely substantially larger than $\log^3 c$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Values of Newform Dedekind Sums Corbett, Georgia Young, Matthew P. Number Theory 11F20 We study a generalized Dedekind sum $S_{χ_1,χ_2}(a,c)$ attached to newform Eisenstein series $E_{χ_1,χ_2}(z,s)$. Our work shows the Dedekind sum is rarely substantially larger than $\log^3 c$. 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. |
| title | Large Values of Newform Dedekind Sums |
| topic | Number Theory 11F20 |
| url | https://arxiv.org/abs/2405.00274 |