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Weyl's Criterion

A Sequence $\{x_1, x_2, \dots\}$ is Equidistributed Iff

\lim_{N\to\infty} {1\over N} \sum_{n<N} e^{2\pi i m x_n} = 0

for each $m=1$, 2, ....

See also Equidistributed Sequence, Ramanujan's Sum


Pólya, G. and Szegö, G. Problems and Theorems in Analysis I. New York: Springer-Verlag, 1972.

Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 155-156 and 254, 1991.

© 1996-9 Eric W. Weisstein