Almost primes in almost all short intervals II
| Autor: | Matomäki, Kaisa, Teräväinen, Joni |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 376, 5433-5459, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/8869 |
| Popis: | We show that, for almost all $x$, the interval $(x, x+(\log x)^{2.1}]$ contains products of exactly two primes. This improves on a work of the second author that had $3.51$ in place of $2.1$. To obtain this improvement, we prove a new type II estimate. One of the new innovations is to use Heath-Brown's mean value theorem for sparse Dirichlet polynomials. Comment: 26 pages; referee comments incorporated; to appear in Trans. Am. Math. Soc |
| Databáze: | arXiv |
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