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 Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 2, Pages 321–397 (Mi izv1559)

An asymptotic formula for the number of solutions of a nonlinear equation with prime numbers

V. A. Plaksin

Abstract: In the article an asymptotic formula is determined for the number of representations of a natural number as the sum of the squares of four integers, two of which are prime.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:2, 275–348

Bibliographic databases:

UDC: 511
MSC: 10J05, 10B05

Citation: V. A. Plaksin, “An asymptotic formula for the number of solutions of a nonlinear equation with prime numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981), 321–397; Math. USSR-Izv., 18:2 (1982), 275–348

Citation in format AMSBIB
\Bibitem{Pla81} \by V.~A.~Plaksin \paper An~asymptotic formula for the number of solutions of a~nonlinear equation with prime numbers \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1981 \vol 45 \issue 2 \pages 321--397 \mathnet{http://mi.mathnet.ru/izv1559} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=616225} \zmath{https://zbmath.org/?q=an:0482.10045|0461.10042} \transl \jour Math. USSR-Izv. \yr 1982 \vol 18 \issue 2 \pages 275--348 \crossref{https://doi.org/10.1070/IM1982v018n02ABEH001389} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Plaksin, “An asymptotic formula for the number of representations of a natural number by a pair of quadratic forms, the arguments of one of which are prime”, Math. USSR-Izv., 25:3 (1985), 551–572
2. Jianya Liu, Ming-Chit Liu, “Representation of Even Integers as Sums of Squares of Primes and Powers of 2”, Journal of Number Theory, 83:2 (2000), 202
3. D. R. Heath-Brown, D. I. Tolev, “Lagranges four squares theorem with one prime and three almost-prime variables”, crll, 2003:558 (2003), 159
4. Jianya Liu, Trevor D Wooley, Gang Yu, “The quadratic Waring–Goldbach problem”, Journal of Number Theory, 107:2 (2004), 298
5. G. S. Lü, H. W. Sun, “On a generalization of Hua’s theorem with five squares of primes”, Acta Math Hungar, 2008
6. YINGCHUN CAI, “Lagrange'S FOUR SQUARES THEOREM WITH VARIABLES OF SPECIAL TYPE”, Int. J. Number Theory, 06:08 (2010), 1801
7. Yingchun Cai, Minggao Lu, “On the slim exceptional set for the Lagrange four squares theorem”, Acta Math Hung, 2011
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