A Direct Proof of a Theorem of Roth.
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A general discrepancy estimate based on p-adic arithmetics
Peter Hellekalek (2009)
Acta Arithmetica
A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy
Henri Faure, Friedrich Pillichshammer (2013)
Acta Arithmetica
In uniform distribution theory, discrepancy is a quantitative measure for the irregularity of distribution of a sequence modulo one. At the moment the concept of digital (t,s)-sequences as introduced by Niederreiter provides the most powerful constructions of s-dimensional sequences with low discrepancy. In one dimension, recently Faure proved exact formulas for different notions of discrepancy for the subclass of NUT digital (0,1)-sequences. It is the aim of this paper to generalize the concept...
A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary
Werner Georg Nowak (2007)
Acta Arithmetica
A metric discrepancy estimate in higher dimensions using methods.
Kamarul Haili, Hailiza (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
A mixed Monte Carlo and quasi-Monte Carlo sequence for multidimensional integral estimation.
Roşca, Alin V. (2007)
Acta Universitatis Apulensis. Mathematics - Informatics
A new construction of (t,s)-sequences and some improved bounds on their quality parameter
David J. S. Mayor, Harald Niederreiter (2007)
Acta Arithmetica
A new upper bound on the star discrepancy of -sequences.
Kritzer, Peter (2005)
Integers
A note on the figure of merit of 2-dimensional rank 2 lattice rules.
Dick, Josef, Pillichshammer, Friedrich (2005)
Integers
A notion of diaphony based on p-adic arithmetic
Peter Hellekalek (2010)
Acta Arithmetica
A partition of the unit sphere into regions of equal area and small diameter.
Leopardi, Paul (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution
József Beck (1989)
Compositio Mathematica
Almost periodic functions and uniform distribution mod 1.
Harald Niederreiter, J. Schoißengeier (1977)
Journal für die reine und angewandte Mathematik
An improved result on irregularities in distribution of sequences of integers
John H. Hodges (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
An L¹ estimate for half-space discrepancy
William W. L. Chen, Giancarlo Travaglini (2011)
Acta Arithmetica
Approximations diophantiennes et problèmes additifs dans les groupes abéliens localement compacts
Jean-Pierre Schreiber (1973)
Bulletin de la Société Mathématique de France
Asimptotic Distribution and Weak Convergence on Compact Riemannian Manifolds.
Martin Blümlinger (1990)
Monatshefte für Mathematik
Bounded remainder sets
Sébastien Ferenczi (1992)
Acta Arithmetica
Bounds for digital nets and sequences
Wolfgang Ch. Schmid, Reinhard Wolf (1997)
Acta Arithmetica
Bounds for the average -extreme and the -extreme discrepancy.
Gnewuch, Michael (2005)
The Electronic Journal of Combinatorics [electronic only]
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