A Density Theorem for Higher Order Sums of Prime Numbers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912102805929984 |
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| author | Lacey, Michael T. Mousavi, Hamed Rahimi, Yaghoub Vempati, Manasa N. |
| author_facet | Lacey, Michael T. Mousavi, Hamed Rahimi, Yaghoub Vempati, Manasa N. |
| contents | Let $P$ be a subset of the primes of lower density strictly larger than $\frac12$. Then, every sufficiently large even integer is a sum of four primes from the set $P$. We establish similar results for $k$-summands, with $k\geq 4$, and for $k \geq 4$ distinct subsets of primes. This extends the work of H.~Li, H.~Pan, as well as X.~Shao on sums of three primes, and A.~Alsteri and X.~Shao on sums of two primes. The primary new contributions come from elementary combinatorial lemmas. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_01296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Density Theorem for Higher Order Sums of Prime Numbers Lacey, Michael T. Mousavi, Hamed Rahimi, Yaghoub Vempati, Manasa N. Number Theory Let $P$ be a subset of the primes of lower density strictly larger than $\frac12$. Then, every sufficiently large even integer is a sum of four primes from the set $P$. We establish similar results for $k$-summands, with $k\geq 4$, and for $k \geq 4$ distinct subsets of primes. This extends the work of H.~Li, H.~Pan, as well as X.~Shao on sums of three primes, and A.~Alsteri and X.~Shao on sums of two primes. The primary new contributions come from elementary combinatorial lemmas. |
| title | A Density Theorem for Higher Order Sums of Prime Numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.01296 |