Abstract:
A new theorem is obtained on the mean value of the number of representations of natural numbers n as the sum of a prime and a perfect square, from which it is deduced that there are at most Ne−a√logN, a>0, natural numbers n⩽N not representable as such a sum.
Bibliography: 17 titles.
\Bibitem{Pol81}
\by I.~V.~Polyakov
\paper On~the exceptional set for the sum of a~prime and a~perfect square
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 3
\pages 611--641
\mathnet{http://mi.mathnet.ru/eng/im1717}
\crossref{https://doi.org/10.1070/IM1982v019n03ABEH001429}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=641805}
\zmath{https://zbmath.org/?q=an:0501.10049|0478.10033}
Linking options:
https://www.mathnet.ru/eng/im1717
https://doi.org/10.1070/IM1982v019n03ABEH001429
https://www.mathnet.ru/eng/im/v45/i6/p1391
This publication is cited in the following 1 articles:
R. Brünner, A. Perelli, J. Pintz, “The exceptional set for the sum of a prime and a square”, Acta Math Hungar, 53:3-4 (1989), 347
Citation in format AMSBIB
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