Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917584782229504 |
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| author | Li, Runbo |
| author_facet | Li, Runbo |
| contents | We provide a new hybrid estimation of single exponential sums, combining Van der Corput, Huxley and Bourgain's result. We also focus on primes in short intervals $(x-x^α,x]$ under the assumption of the existence of exceptional Dirichlet characters and get a small improvement of a 2004 result of Friedlander and Iwaniec. By using our new estimation of exponential sums, we extend the previous admissible range $0.4937 \leqslant α\leqslant 1$ to $0.4923 \leqslant α\leqslant 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals Li, Runbo Number Theory We provide a new hybrid estimation of single exponential sums, combining Van der Corput, Huxley and Bourgain's result. We also focus on primes in short intervals $(x-x^α,x]$ under the assumption of the existence of exceptional Dirichlet characters and get a small improvement of a 2004 result of Friedlander and Iwaniec. By using our new estimation of exponential sums, we extend the previous admissible range $0.4937 \leqslant α\leqslant 1$ to $0.4923 \leqslant α\leqslant 1$. |
| title | Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.11139 |