Geodesic
The Hardy--Littlewood problem for numbers with a~fixed number of prime divisors
Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1283-1309

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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 $(2+\varepsilon)\ln\ln N\leqslant k\leqslant b\ln\ln N$. 
@article{IM2_1995_59_6_a8,
     author = {N. M. Timofeev},
     title = {The {Hardy--Littlewood} problem for numbers with a~fixed number of prime divisors},
     journal = {Izvestiya. Mathematics },
     pages = {1283--1309},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_6_a8/}
}
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N. M. Timofeev. The Hardy--Littlewood problem for numbers with a~fixed number of prime divisors. Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1283-1309. http://geodesic.mathdoc.fr/item/IM2_1995_59_6_a8/