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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 67–78 (Mi izv1471)

The number of integers representable as a sum of two squares on small intervals

V. A. Plaksin

Abstract: Let $M(m,h)$ denote the number of natural numbers in the interval $(m;m+h)$ which are representable as a sum of two squares. Under the condition $n>\ln^{42,5+\varepsilon}X$, $\varepsilon>0$, a best possible lower bound for $M(m,h)$ is established for almost all $m\leqslant X$ (for all but $o(X)$).
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 67–78

Bibliographic databases:

UDC: 511
MSC: Primary 11N25; Secondary 11E25, 11N35, 11N37

Citation: V. A. Plaksin, “The number of integers representable as a sum of two squares on small intervals”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 67–78; Math. USSR-Izv., 28:1 (1987), 67–78

Citation in format AMSBIB
\Bibitem{Pla86} \by V.~A.~Plaksin \paper The number of integers representable as a~sum of two squares on small intervals \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 1 \pages 67--78 \mathnet{http://mi.mathnet.ru/izv1471} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=835566} \zmath{https://zbmath.org/?q=an:0615.10062|0597.10045} \transl \jour Math. USSR-Izv. \yr 1987 \vol 28 \issue 1 \pages 67--78 \crossref{https://doi.org/10.1070/IM1987v028n01ABEH000867} 

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This publication is cited in the following articles:
1. V. A. Plaksin, “The distribution of numbers representable as a sum of two squares”, Math. USSR-Izv., 31:1 (1988), 171–191
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