On the Sum of Additive Characters and its Applications over Finite Fields
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908588572672000 |
|---|---|
| author | K., Maithri R., Vadiraja Bhatta G. P, Indira K. |
| author_facet | K., Maithri R., Vadiraja Bhatta G. P, Indira K. |
| contents | In this paper, we study the sum of additive characters over finite fields, with a focus on those of specified \(\mathbb{F}_q\)-Order. We establish a general formula for these character sums, providing an additive analogue to classical results previously known for multiplicative characters. As an application, we derive a Möbius function \(μ(g)\) for polynomials \(g \in \mathbb{F}_q[x]\), analogous to the integer Möbius function \(μ(n)\), and develop a characteristic function for \(k\)-normal elements. We also generalize several classical identities from the integer setting to the polynomial setting, highlighting the structural parallels between these two domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Sum of Additive Characters and its Applications over Finite Fields K., Maithri R., Vadiraja Bhatta G. P, Indira K. Number Theory 11T30, 11T06, 11T23, 12E20 In this paper, we study the sum of additive characters over finite fields, with a focus on those of specified \(\mathbb{F}_q\)-Order. We establish a general formula for these character sums, providing an additive analogue to classical results previously known for multiplicative characters. As an application, we derive a Möbius function \(μ(g)\) for polynomials \(g \in \mathbb{F}_q[x]\), analogous to the integer Möbius function \(μ(n)\), and develop a characteristic function for \(k\)-normal elements. We also generalize several classical identities from the integer setting to the polynomial setting, highlighting the structural parallels between these two domains. |
| title | On the Sum of Additive Characters and its Applications over Finite Fields |
| topic | Number Theory 11T30, 11T06, 11T23, 12E20 |
| url | https://arxiv.org/abs/2506.16081 |