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

This article is cited in 7 scientific papers (total in 7 papers)

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.

Full text: PDF file (5363 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:2, 275–348

Bibliographic databases:

UDC: 511
MSC: 10J05, 10B05
Received: 04.11.1980

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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  mathscinet  zmath
    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  crossref
    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  crossref  mathscinet  zmath
    4. Jianya Liu, Trevor D Wooley, Gang Yu, “The quadratic Waring–Goldbach problem”, Journal of Number Theory, 107:2 (2004), 298  crossref
    5. G. S. Lü, H. W. Sun, “On a generalization of Hua’s theorem with five squares of primes”, Acta Math Hungar, 2008  crossref  isi
    6. YINGCHUN CAI, “Lagrange'S FOUR SQUARES THEOREM WITH VARIABLES OF SPECIAL TYPE”, Int. J. Number Theory, 06:08 (2010), 1801  crossref
    7. Yingchun Cai, Minggao Lu, “On the slim exceptional set for the Lagrange four squares theorem”, Acta Math Hung, 2011  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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