Martin Ortiz Ramirez
Published 2019-12-22Version 1
We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the segment by hyperplanes of rational direction, and then cover an arbitrary segment with one having rational direction. Diophantine approximation can be used to obtain the best rational direction possible.
Upper bounds for prime gaps related to Firoozbakht's conjecture
Maximal ratio of coefficients of divisors and an upper bound for height for rational maps
An upper bound for Davenport constant of finite groups
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