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Counting Lattice Points in The Sphere
Author(s) -
Tsang KaiMan
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609300007505
Subject(s) - mathematics , mathematics subject classification , combinatorics , lattice (music) , upper and lower bounds , radius , mathematical analysis , physics , computer security , computer science , acoustics
We consider the error termP 3 ( R ) = # { n ∈ Z 3 : | n | ⩽ R } − 4 3 π R 3which occurs in the counting of lattice points in a sphere of radius R . By considering second and third power moments, we prove thatP 3 ( R ) = Ω ± ( R l o g R) . An upper bound for the gap between the sign changes of P 3 ( R ) is also proved. 1991 Mathematics Subject Classification 11P21.
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