This article is cited in 4 papers

The Hardy–Littlewood problem for numbers with a fixed number of prime divisors

N. M. Timofeev

Vladimir State Pedagogical University

Abstract: In this paper we investigate the number of representations of a natural number $N$ as the sum of a number with $k$ prime divisors and two squares, where $k$ may depend on $N$. We determine the asymptotic behaviour when $2\leqslant k\leqslant(2-\varepsilon)\ln\ln N$ and $(2+\varepsilon)\ln\ln N\leqslant k\leqslant b\ln\ln N$.

MSC: 11P55, 11D85, 11P32, 11N25

Received: 05.12.1994

 English version: Izvestiya: Mathematics, 1995, 59:6, 1283–1309

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