Polynomial bounds for the Chowla Cosine Problem
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911170954264576 |
|---|---|
| author | Bedert, Benjamin |
| author_facet | Bedert, Benjamin |
| contents | Let $A\subset \mathbf{N}$ be a finite set of $n=|A|$ positive integers, and consider the cosine sum $f_A(x)=\sum_{a\in A}\cos ax$. We prove that $$\min_x f_A(x)\leqslant -n^{ 1/7-o(1)},$$ thereby establishing polynomial bounds for the Chowla cosine problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial bounds for the Chowla Cosine Problem Bedert, Benjamin Classical Analysis and ODEs Combinatorics Number Theory Let $A\subset \mathbf{N}$ be a finite set of $n=|A|$ positive integers, and consider the cosine sum $f_A(x)=\sum_{a\in A}\cos ax$. We prove that $$\min_x f_A(x)\leqslant -n^{ 1/7-o(1)},$$ thereby establishing polynomial bounds for the Chowla cosine problem. |
| title | Polynomial bounds for the Chowla Cosine Problem |
| topic | Classical Analysis and ODEs Combinatorics Number Theory |
| url | https://arxiv.org/abs/2509.05260 |