Dupain, Yves Discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\). (Discrépance de la suite \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\).) (French) Zbl 0386.10021 Ann. Inst. Fourier 29, No. 1, 81-106 (1979). Let \(D^*(N)\) be the star-discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\). We show that\[ \limsup {D^*(N)\over \log N} = {3\over 20} \Big(\log{1+\sqrt 5\over 2}\Big) ^{-1} = 0.31\cdots, \] which illustrates the fact that our sequence has smaller star-discrepancy than that of van der Corput’s sequence. Our proofs involve continued fraction theory. Reviewer: Yves Dupain Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 11K06 General theory of distribution modulo \(1\) 11K31 Special sequences Keywords:star discrepancy; uniform distribution PDF BibTeX XML Cite \textit{Y. Dupain}, Ann. Inst. Fourier 29, No. 1, 81--106 (1979; Zbl 0386.10021) Full Text: DOI Numdam EuDML OpenURL References: [1] R. BEJIAN et H. FAURE, Discrépance de la suite de Van der Corput, C.R. Acad. Sc., Paris, 285 (1977), 313-316. · Zbl 0361.10032 [2] Y. DUPAIN, Intervalles à restes majorés pour la suite {nα}, Acta. Math. Acad. Scient. Hung., t. 29 (3,4) (1977), 289-303. · Zbl 0372.10026 [3] L. KUIPERS and H. NIEDERREITER, Uniform distribution of sequences, Wiley Interscience, New York, (1974), 88-132. · Zbl 0281.10001 [4] J. LESCA, Sur la répartition modulo 1 des suites {nα}, Acta Arith., 20 (1972), 345-352. · Zbl 0239.10018 [5] J. LESCA, Sur la répartition modulo 1 des suites {nα}, Séminaire Delange-Pisot-Poitou, (1966-1967), fascicule 1, exposé n° 2. · Zbl 0164.05502 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.