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.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{MEM_2024_53_a3,
     author = {Todorova, Tatyana L.},
     title = {On the distribution of \ensuremath{\alpha}p^2 + \ensuremath{\beta} modulo one for primes p such that p + 2 has no more two prime divisors},
     journal = {Mathematics and Education in Mathematics},
     pages = {39--56},
     publisher = {mathdoc},
     volume = {53},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2024_53_a3/}
}
TY  - JOUR
AU  - Todorova, Tatyana L.
TI  - On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors
JO  - Mathematics and Education in Mathematics
PY  - 2024
SP  - 39
EP  - 56
VL  - 53
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MEM_2024_53_a3/
LA  - en
ID  - MEM_2024_53_a3
ER  - 
%0 Journal Article
%A Todorova, Tatyana L.
%T On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors
%J Mathematics and Education in Mathematics
%D 2024
%P 39-56
%V 53
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MEM_2024_53_a3/
%G en
%F MEM_2024_53_a3
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/