Eine effektive Absch"atzung f"ur die Gitter-Diskrepanz von Rotationsellipsoiden

Details Eine effektive Absch"atzung f"ur die Gitter-Diskrepanz von Rotationsellipsoiden Eine effektive Absch"atzung f"ur die Gitter-Diskrepanz von Rotationsellipsoiden

2006-03-13

arxiv.org/abs/math/0603292v1

Mathematics

Number Theory

17 pages

Scientific paper

An effective estimate for the lattice point discrepancy of ellipsoids of rotation. This paper provides an explicit bound, with numerical constants, for the lattice point discrepancy (= number of integer points minus volume) of an ellipsoid Q < x, where Q is a positive definite ternary quadratic form, diagonalized and invariant with respect to rotations around one coordinate axis. In the result the exponent of x in the leading term is equal to 11/16.

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