Almost primes in almost all short intervals II
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911990161604608 |
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| author | Matomäki, Kaisa Teräväinen, Joni |
| author_facet | Matomäki, Kaisa Teräväinen, Joni |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05038 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Almost primes in almost all short intervals II Matomäki, Kaisa Teräväinen, Joni Number Theory 11N05, 11N36 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. |
| title | Almost primes in almost all short intervals II |
| topic | Number Theory 11N05, 11N36 |
| url | https://arxiv.org/abs/2207.05038 |