This article is cited in 6 papers

The distribution of Hardy–Littlewood numbers in arithmetic progressions

Z. Kh. Rakhmonov


Abstract: An asymptotic formula is obtained for the number of solutions of the congruence
$$ p+n^2\equiv l\ (\operatorname{mod}D),\qquad p\leqslant x,\quad n\leqslant\sqrt x,\quad(l,D)=1, $$
where $D$ is a sufficiently large prime.
Bibliography: 7 titles.

UDC: 511

MSC: 11N64, 11N37

Received: 15.06.1987

 English version: Mathematics of the USSR-Izvestiya, 1990, 34:1, 213–228

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