Poisson Approximation of prime divisors of shifted primes
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915738494697472 |
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| author | Ford, Kevin |
| author_facet | Ford, Kevin |
| contents | We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shifted primes in disjoint sets behave like independent Poisson variables. As a consequence, we establish a transference principle between the anatomy of random integers up to x and of random shifted primes p+a with p < x. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson Approximation of prime divisors of shifted primes Ford, Kevin Number Theory 11N05, 11N25, 11N35, 11K65 We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shifted primes in disjoint sets behave like independent Poisson variables. As a consequence, we establish a transference principle between the anatomy of random integers up to x and of random shifted primes p+a with p < x. |
| title | Poisson Approximation of prime divisors of shifted primes |
| topic | Number Theory 11N05, 11N25, 11N35, 11K65 |
| url | https://arxiv.org/abs/2408.03803 |