A Generalized Elliott-Halberstam Conjecture Implying the Twin Prime Hypothesis
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908663213457408 |
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| author | Smith, Trey |
| author_facet | Smith, Trey |
| contents | We propose a generalization of the Elliott-Halberstam conjecture concerning the distribution of prime pairs in arithmetic progressions. This conjecture, which we call the Generalized Elliott-Halberstam Conjecture for Shifted Convolutions (GEH-2), provides a level of distribution for correlations of the von Mangoldt function. We show that GEH-2 implies the twin prime conjecture, describe heuristic and analytic motivation, and discuss implications for prime gaps and $k$-tuple patterns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalized Elliott-Halberstam Conjecture Implying the Twin Prime Hypothesis Smith, Trey Number Theory We propose a generalization of the Elliott-Halberstam conjecture concerning the distribution of prime pairs in arithmetic progressions. This conjecture, which we call the Generalized Elliott-Halberstam Conjecture for Shifted Convolutions (GEH-2), provides a level of distribution for correlations of the von Mangoldt function. We show that GEH-2 implies the twin prime conjecture, describe heuristic and analytic motivation, and discuss implications for prime gaps and $k$-tuple patterns. |
| title | A Generalized Elliott-Halberstam Conjecture Implying the Twin Prime Hypothesis |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.14810 |