The L2 Discrepancy of Two-Dimensional Lattices

Dmitriy Bilyk, Vladimir N. Temlyakov, Rui Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Let α be an irrational number with bounded partial quotients of the continued fraction ak. It is well known that symmetrizations of the irrational lattice have optimal order of L2 discrepancy, √log N. The same is true for their rational approximations, where pn/qn is the nth convergent of α. However, the question whether and when the symmetrization is really necessary remained wide open. We show that the L2 discrepancy of the nonsymmetrized lattice Ln(α) grows as in particular, characterizing the lattices for which the L2 discrepancy is optimal.

Original languageEnglish (US)
Title of host publicationRecent Advances in Harmonic Analysis and Applications
Subtitle of host publicationIn Honor of Konstantin Oskolkov
PublisherSpringer New York LLC
Pages63-77
Number of pages15
ISBN (Print)9781461445647
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume25
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

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