Distribution of
α
p
2
Modulo One with Prime Variable
p
of a Special Form
Let P r denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that, for α ∈ ℝ / ℚ , β ∈ ℝ , and 0 < θ < 10 / 1561 , there exist infinitely many primes p , such that α p 2 + β < p − θ and p + 2 = P 4 , which constitutes an improvement upon the previous result.
Keyword(s):
2018 ◽
Vol 14
(06)
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pp. 1669-1687
2010 ◽
Vol 06
(08)
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pp. 1801-1817
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2018 ◽
Vol 14
(09)
◽
pp. 2425-2440
2013 ◽
Vol 50
(4)
◽
pp. 470-490
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Keyword(s):
2011 ◽
Vol 07
(05)
◽
pp. 1359-1378
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