Abstract
Let r(n) count the number of representations of a positive integer n as a sum of two integer squares. We prove a truncated Voronoi-type formula for the twisted Mobius transform
where k and l are positive integers such that k and 4l are coprime, and give some applications (almost periodicity, limit distribution, an asymptotic mean-square formula, and O- and Ω-estimates for the error term).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1405 – 1418, October, 2004.
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Slezeviciene, R., Steuding, J. On Exponential Sums Related to the Circle Problem. Ukr Math J 56, 1676–1692 (2004). https://doi.org/10.1007/s11253-005-0143-5
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DOI: https://doi.org/10.1007/s11253-005-0143-5