The Kloosterman sums on the ellipse
The main point of our research is to obtain the estimates for Kloosterman sums \(\widetilde{K}(\alpha,\beta;h,q;k)\) considered on the ellipse bound for the case of the integer rational module \(q\) and for some natural number \(k\) with conditions \((\alpha,q)=(\beta,q)=1\) on the integer numbers o...
Збережено в:
| Видавець: | Lugansk National Taras Shevchenko University |
|---|---|
| Дата: | 2023 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2048 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
Організація
Algebra and Discrete Mathematics| Резюме: | The main point of our research is to obtain the estimates for Kloosterman sums \(\widetilde{K}(\alpha,\beta;h,q;k)\) considered on the ellipse bound for the case of the integer rational module \(q\) and for some natural number \(k\) with conditions \((\alpha,q)=(\beta,q)=1\) on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function \(\tau_\ell(\alpha)\) for \(\ell=2,3,\ldots\) over the ring of integer elements of imaginary quadratic field in arithmetic progression. |
|---|