An explicit formula for the \(L_2\)-discrepancy of \((n\alpha)\)-sequences

DOI10.1007/s00607-005-0143-1zbMath1099.11038OpenAlexW2044021661MaRDI QIDQ818850

Johannes Schoissengeier, Luís Roçadas

Publication date: 21 March 2006

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-005-0143-1

zbMATH Keywords

continued fractionsdiscrepancydistribution mod\,1Weyl sequence

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Irregularities of distribution, discrepancy (11K38) Metric theory of continued fractions (11K50) Distribution modulo one (11J71) Special sequences (11K31)

Cites Work

• Calculation of improper integrals using \((n\alpha)\)-sequences
• Another proof of a theorem of J. Beck
• Continued fractions and density results for Dedekind sums.
• Efficient algorithms for computing the $L_2$-discrepancy