In:
International Journal of Number Theory, World Scientific Pub Co Pte Ltd, Vol. 19, No. 03 ( 2023-04), p. 511-529
Kurzfassung:
Let [Formula: see text] be a nonempty finite subset of [Formula: see text] and [Formula: see text] be an arbitrary map (choice of signs for [Formula: see text] ). We will say that [Formula: see text] has residue pattern [Formula: see text] modulo [Formula: see text] if [Formula: see text] , where [Formula: see text] is the Legendre symbol mod [Formula: see text] . For a given nonempty finite subset [Formula: see text] of [Formula: see text] with a choice of signs [Formula: see text] and a real number [Formula: see text] , we obtain an asymptotic formula for the number of primes [Formula: see text] of the form [Formula: see text] such that [Formula: see text] has residue pattern [Formula: see text] modulo [Formula: see text] which also satisfies [Formula: see text] where [Formula: see text] are integers with [Formula: see text] and [Formula: see text]. For an irrational [Formula: see text] and a real [Formula: see text], we also obtain an asymptotic formula for the same but primes [Formula: see text] of the form [Formula: see text] under certain assumption on [Formula: see text] .
Materialart:
Online-Ressource
ISSN:
1793-0421
,
1793-7310
DOI:
10.1142/S1793042123500240
Sprache:
Englisch
Verlag:
World Scientific Pub Co Pte Ltd
Publikationsdatum:
2023
SSG:
17,1
