Geodesic
The Hardy--Littlewood conjecture. An algebraic approach
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 5-10

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We consider the well-known Hardy–Littlewood equation, which is related to the Waring problem, in terms of roots of polynomials of the corresponding degree. The Hardy–Littlewood conjecture is confirmed for cubic fields. Bibliography: 3 titles. 
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     author = {A. I. Vinogradov},
     title = {The {Hardy--Littlewood} conjecture. {An} algebraic approach},
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     volume = {204},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a0/}
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A. I. Vinogradov. The Hardy--Littlewood conjecture. An algebraic approach. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 5-10. http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a0/