Covering shrinking polynomials by quasi progressions
| Autor: | Hegyvári, Norbert |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Erd\H os introduced the quantity $S=T\sum^T_{i=1}X_i$, where $X_1,\dots, X_T$ are arithmetic progressions, and cover the square numbers up to $N$. He conjectured that $S$ is close to $N$, i.e. the square numbers cannot be covered "economically" by arithmetic progressions. S\'ark\"ozy confirmed this conjecture and proved that $S\geq cN/\log^2N$. In this paper, we extend this to shrinking polynomials and so-called $\{X_i\}$ quasi progressions. Comment: 10 pages comments are welcome |
| Databáze: | arXiv |
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