A note on bilinear sums with modular square roots
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917463035215872 |
|---|---|
| author | Baier, Stephan |
| author_facet | Baier, Stephan |
| contents | Bag and Shparlinski \cite{BaSh} considered bilinear sums of terms of the form $e_p(axy^s)$, where $p$ is a prime, $a$ is an integer coprime to $p$, $s$ is an integer, $x$ runs over a subset of $\mathbb{F}_p^{\ast}$ and $y$ runs over an interval. Closely following their method, we establish an analogous result for the case when $s=1/2$ ($y^{1/2}$ being a modular square root of $y$ modulo $p$, if existent). A part of this note is devoted to reviewing our recent works on related bilinear sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01635 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on bilinear sums with modular square roots Baier, Stephan Number Theory 11L05, 11L07, 11L26, 11L40 Bag and Shparlinski \cite{BaSh} considered bilinear sums of terms of the form $e_p(axy^s)$, where $p$ is a prime, $a$ is an integer coprime to $p$, $s$ is an integer, $x$ runs over a subset of $\mathbb{F}_p^{\ast}$ and $y$ runs over an interval. Closely following their method, we establish an analogous result for the case when $s=1/2$ ($y^{1/2}$ being a modular square root of $y$ modulo $p$, if existent). A part of this note is devoted to reviewing our recent works on related bilinear sums. |
| title | A note on bilinear sums with modular square roots |
| topic | Number Theory 11L05, 11L07, 11L26, 11L40 |
| url | https://arxiv.org/abs/2605.01635 |