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NUMBER OF LATTICE POINTS ON A SHELL WITH PRESCRIBED NORMS
Keywords:
lattice points, sum of squares representation, counting function.DOI:
https://doi.org/10.17654/0972087124003Abstract
The purpose of this short note is to give an upper estimate of the number of lattice points in shrinking shells with norm controlled by an auxiliary function decaying at infinity.
Received: September 26, 2023
Revised: October 16, 2023
Accepted: October 26, 2023
References
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E. Grosswald, Representation of Integers as Sums of Squares, Springer-Verlag, New York, Inc., 1985.
J. E. Littlewood, On the class number of the corpus sqrt[P]{-k}, Proc. Lond. Math. Soc. 27 (1928), 358-372.
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