On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors
DOI:
https://doi.org/10.55630/mem.2024.53.039-056Keywords:
linear sieve, almost primes, distribution modulo oneAbstract
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.
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