Expander estimates for cubes
| Autor: | Bruedern, Joerg, Myerson, Simon L Rydin |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | If $\mathscr A$ is a set of natural numbers of exponential density $\delta$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 \delta)$. This is a considerable improvement on the previous best lower bounds for this problem, obtained by Davenport more than 80 years ago. The result is the best possible for $\delta\ge \frac 45$. Comment: 27 pages, 16 references |
| Databáze: | arXiv |
| Externí odkaz: |
|