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Description

High Quality Content by WIKIPEDIA articles! In mathematics, in the theory of diophantine approximation, Weyl's criterion states that a sequence (xn) of real numbers is equidistributed mod 1 if and only if for all non-zero integers ell we have: lim_{nrightarrowinfty}frac{1}{n}sum_{j=0}^{n-1}e^{2piimathell x_{j}}=0. Therefore distribution questions can be reduced to bounds on exponential sums, a fundamental and general method. This extends naturally to higher dimensions. We say a sequence x_{n}inmathbb{R}^{k} is equidistributed mod 1 if and only if forall ellinmathbb{Z}^{k}backslash{0} we have: lim_{nrightarrowinfty}frac{1}{n}sum_{j=0}^{n-1}e^{2piimath(ell cdot x_{j})}=0. The criterion is named after, and was first formulated by, Hermann Weyl.

Contributors

Editor Lambert M. Surhone

Editor Miriam T. Timpledon

Editor Susan F. Marseken

Product Details

DUIN 708MCMU4QHG

GTIN 9786131188176

Language English

Pages 88

Product type Paperback

Weyl's Criterion

Lambert M. Surhone

$32.59

Seller: Dodax EU

Delivery date: between Wednesday, August 12 and Friday, August 14

Condition: New

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