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Visible lattice points in the sphere

✍ Scribed by Fernando Chamizo; Elena Cristóbal; Adrián Ubis

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
146 KB
Volume
126
Category
Article
ISSN
0022-314X

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✦ Synopsis

The number of visible (primitive) lattice points in the sphere of radius R is well approximated by 4π 3ζ(3) R 3 . We consider an integral expression involving the error term E * (R), which leads to

). This is comparable to what is known in the sphere problem. We can avoid the use of the second power moment (which is in this case unknown) by employing an auxiliary trigonometric series correlated to E * (R). This approach to prove Ω-results seems to be new and could be useful in other problems.

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