Geodesic
On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors
Mathematics and Education in Mathematics, Tome 53 (2024), pp. 39-56 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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A classical problem in analytic number theory is to study the distribution of frac- tional part αp^k + β, k ≥ 1 modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p + 2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property. Класически проблем в аналитичната теория на числата е проблемът за разп- ределението на дробните части на числата αp^k + β, k ≥ 1, където α е ирационално и p пробягва множеството на простите числа. Ние разглеждаме подмножество на множеството на простите числа p, за които p + 2 е почти просто и доказваме, че тяхното разпределение има свойства подобни на тези на разпределението на простите числа.
Keywords: linear sieve, almost primes, distribution modulo one, 11J71, 11N36, линейно решето, почти прости, разпределение по модул 1, 11J71, 11N36 
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Todorova, Tatyana L. On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors. Mathematics and Education in Mathematics, Tome 53 (2024), pp. 39-56. http://geodesic.mathdoc.fr/item/MEM_2024_53_a3/