Primes with a missing digit: distribution in arithmetic progressions and an application in sieve theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909112615305216 |
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| author | Nath, Kunjakanan |
| author_facet | Nath, Kunjakanan |
| contents | We prove Bombieri-Vinogradov type theorems for primes with a missing digit in their $b$-adic expansion for some large positive integer $b$. The proof is based on the circle method, which relies on the Fourier structure of the integers with a missing digit and the exponential sums over primes in arithmetic progressions. Combining our results with the semi-linear sieve, we obtain an upper bound and a lower bound of the correct order of magnitude for the number of primes of the form $p=1+m^2+n^2$ with a missing digit in a large odd base $b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_09212 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Primes with a missing digit: distribution in arithmetic progressions and an application in sieve theory Nath, Kunjakanan Number Theory We prove Bombieri-Vinogradov type theorems for primes with a missing digit in their $b$-adic expansion for some large positive integer $b$. The proof is based on the circle method, which relies on the Fourier structure of the integers with a missing digit and the exponential sums over primes in arithmetic progressions. Combining our results with the semi-linear sieve, we obtain an upper bound and a lower bound of the correct order of magnitude for the number of primes of the form $p=1+m^2+n^2$ with a missing digit in a large odd base $b$. |
| title | Primes with a missing digit: distribution in arithmetic progressions and an application in sieve theory |
| topic | Number Theory |
| url | https://arxiv.org/abs/2108.09212 |