تقرير
Counting Divisors in the Outputs of a Binary Quadratic Form
| العنوان: | Counting Divisors in the Outputs of a Binary Quadratic Form |
|---|---|
| المؤلفون: | Kuan, Chan Ieong, Lowry-Duda, David, Walker, Alexander, Huang, Tinghao |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11F30, 11N37, 11F72 |
| الوصف: | For a fixed natural number $h$, we prove meromorphic continuation of the two-variable Dirichlet series $\sum_m r_2(m) \sigma_w(m + h) (m + h)^{-s + w}$ to $\mathbb{C}^2$ and use this to obtain asymptotics for $\sum_{m^2 + n^2 \leq X} \sigma_w(m^2 + n^2 + h)$. We approach this continuation through spectral theory. Our results are comparable to earlier work of Bykovskii, who used different methods to study the sums $\sum_{n^2 \leq X} \sigma_w(n^2 + h)$. Comment: 41 pages, including an appendix by Kuan and Huang |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.13632 |
| رقم الأكسشن: | edsarx.2310.13632 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |