Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14795 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this note, we investigate the paratrophic determinants attached to the multiplicative semigroup $\mathbb{Z}/N\mathbb{Z}$. We show that, via discrete Fourier, cosine, and sine transforms, these determinants factor into products of group determinants indexed by $d|N$. This yields explicit formulas for several determinant families, including determinants involving periodic Bernoulli functions and powers of the tangent function. As an application, we also prove a corrected version of a conjecture of Sun Zhi-Wei.