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Lattice Points in the Circle and Sphere

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Let P(x) and P 3 (x) be the error terms in the Gaussian circle problem and the sphere problem, respectively.

We investigate the asymptotic behavior of the sums

$$ {\displaystyle \sum_{\underset{k\equiv 0\left( \mod p\right)}{k\le 0}} P(k),}\;{\displaystyle \sum_{\underset{k\equiv 0\left( \mod p\right)}{k\le x}}{P}_3(k).} $$

Here, p ≥ 2 is a prime number. Bibliography: 20 titles.

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    O. M. Fomenko

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  1. O. M. Fomenko
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Correspondence to O. M. Fomenko.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 418, 2013, pp. 198–220.

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Fomenko, O.M. Lattice Points in the Circle and Sphere. J Math Sci 200, 632–645 (2014). https://doi.org/10.1007/s10958-014-1953-5

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