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LOWER BOUNDS FOR ${L}_{1} $ DISCREPANCY

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  18 March 2013

Armen Vagharshakyan
Armen Vagharshakyan*
Affiliation:
Mathematics Department, Brown University, 151 Thayer St, Providence, RI 02912, U.S.A. email armen@math.brown.edu

Abstract

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We find the best asymptotic lower bounds for the coefficient of the leading term of the ${L}_{1} $ norm of the two-dimensional axis-parallel discrepancy that can be obtained by Roth’s orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, and complex and harmonic analysis.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy

Information

Type
Research Article
Information
Mathematika , Volume 59 , Issue 2 , July 2013 , pp. 365 - 379
Copyright
Copyright © University College London 2013 

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