An average Brun-Titchmarsh theorem and shifted primes with a large prime factor
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911194691928064 |
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| author | Li, Runbo |
| author_facet | Li, Runbo |
| contents | The author studies an average version of Brun-Titchmarsh theorem with large moduli. Using Maynard's recent breakthrough on the Bombieri-Friedlander-Iwaniec type triple convolution estimates, we refine the previous result of Baker and Harman (1996). As an application, we improve a result of Baker and Harman (1998) on shifted primes with a large prime factor, showing that the largest prime factor of $p - 1$ is larger than $p^{0.679}$ for infinitely many primes $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An average Brun-Titchmarsh theorem and shifted primes with a large prime factor Li, Runbo Number Theory The author studies an average version of Brun-Titchmarsh theorem with large moduli. Using Maynard's recent breakthrough on the Bombieri-Friedlander-Iwaniec type triple convolution estimates, we refine the previous result of Baker and Harman (1996). As an application, we improve a result of Baker and Harman (1998) on shifted primes with a large prime factor, showing that the largest prime factor of $p - 1$ is larger than $p^{0.679}$ for infinitely many primes $p$. |
| title | An average Brun-Titchmarsh theorem and shifted primes with a large prime factor |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.18285 |