Pseudofinite fields with additive and multiplicative character
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909924282335232 |
|---|---|
| author | Ludwig, Stefan Marian |
| author_facet | Ludwig, Stefan Marian |
| contents | We introduce the theory $\mathrm{PF}^{+,\times}$ of pseudofinite fields with generic additive and multiplicative character added as continuous logic predicates. Using the Weil bounds on character sums over finite fields as well as the Erdős-Turàn-Koksma inequality we show that it is the asymptotic theory (in characteristic $0$) of finite fields with (sufficiently generic) additive and multiplicative character. Moreover, we establish quantifier elimination in a natural definitional expansion of the language and deduce that integration by the Chatzidakis-van den Dries-Macintyre counting measure is uniformly definable in the parameters. Finally, we show that $\mathrm{PF}^{+,\times}$ is a simple theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudofinite fields with additive and multiplicative character Ludwig, Stefan Marian Logic Primary 03C60, Secondary 11L40, 12E20 We introduce the theory $\mathrm{PF}^{+,\times}$ of pseudofinite fields with generic additive and multiplicative character added as continuous logic predicates. Using the Weil bounds on character sums over finite fields as well as the Erdős-Turàn-Koksma inequality we show that it is the asymptotic theory (in characteristic $0$) of finite fields with (sufficiently generic) additive and multiplicative character. Moreover, we establish quantifier elimination in a natural definitional expansion of the language and deduce that integration by the Chatzidakis-van den Dries-Macintyre counting measure is uniformly definable in the parameters. Finally, we show that $\mathrm{PF}^{+,\times}$ is a simple theory. |
| title | Pseudofinite fields with additive and multiplicative character |
| topic | Logic Primary 03C60, Secondary 11L40, 12E20 |
| url | https://arxiv.org/abs/2511.20243 |