On finite pseudorandom binary sequences III: The Liouville function, I
Julien Cassaigne; Sébastien Ferenczi; Christian Mauduit; Jöel Rivat; András Sárközy
Acta Arithmetica (1999)
- Volume: 87, Issue: 4, page 367-390
- ISSN: 0065-1036
Access Full Article
topHow to cite
topJulien Cassaigne, et al. "On finite pseudorandom binary sequences III: The Liouville function, I." Acta Arithmetica 87.4 (1999): 367-390. <http://eudml.org/doc/207226>.
@article{JulienCassaigne1999,
author = {Julien Cassaigne, Sébastien Ferenczi, Christian Mauduit, Jöel Rivat, András Sárközy},
journal = {Acta Arithmetica},
keywords = {finite pseudorandom binary sequences; Liouville function; correlation measure; complexity of sequence; well-distribution measure; pseudorandom properties of arithmetic sequences},
language = {eng},
number = {4},
pages = {367-390},
title = {On finite pseudorandom binary sequences III: The Liouville function, I},
url = {http://eudml.org/doc/207226},
volume = {87},
year = {1999},
}
TY - JOUR
AU - Julien Cassaigne
AU - Sébastien Ferenczi
AU - Christian Mauduit
AU - Jöel Rivat
AU - András Sárközy
TI - On finite pseudorandom binary sequences III: The Liouville function, I
JO - Acta Arithmetica
PY - 1999
VL - 87
IS - 4
SP - 367
EP - 390
LA - eng
KW - finite pseudorandom binary sequences; Liouville function; correlation measure; complexity of sequence; well-distribution measure; pseudorandom properties of arithmetic sequences
UR - http://eudml.org/doc/207226
ER -
References
top- [Ch] S. Chowla, The Riemann Hypothesis and Hilbert's Tenth Problem, Gordon and Breach, New York, 1965. Zbl0136.32702
- [Ell1] P. D. T. A. Elliott, Probabilistic Number Theory, Vol. II, Springer, New York, 1980.
- [Ell2] P. D. T. A. Elliott, On the correlation of multiplicative functions, Notas Soc. Mat. Chile 11 (1992), 1-11.
- [Ell3] P. D. T. A. Elliott, On the correlation of multiplicative and the sum of additive arithmetic functions, Mem. Amer. Math. Soc. 538 (1994).
- [GH] S. W. Graham and D. Hensley, Problem E3025, Amer. Math. Monthly 90 (1983), 707.
- [Ha] G. Halász, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365-403. Zbl0165.05804
- [HR] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
- [HPW] G. Harman, J. Pintz and D. Wolke, A note on the Möbius and the Liouville function, Studia Sci. Math. Hungar. 20 (1985), 295-299. Zbl0544.10041
- [Hi1] A. Hildebrand, Multiplicative functions at consecutive integers, Math. Proc. Cambridge Philos. Soc. 100 (1986), 229-236. Zbl0615.10053
- [Hi2] A. Hildebrand, On consecutive values of the Liouville function, Enseign. Math. 32 (1986), 219-226. Zbl0615.10054
- [Hi3] A. Hildebrand, Math. Reviews, review no. 95d:11099.
- [Li] J.-E. Littlewood, Quelques conséquences de l'hypothèse que la fonction ζ(s) de Riemann n'a pas de zéros dans le demi-plan R(s) > 1/2, C. R. Acad. Sci. Paris 154 (1912), 263-266. Zbl43.0329.02
- [MS1] C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365-377. Zbl0886.11048
- [MS2] C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences II: The Champernowne, Rudin-Shapiro and Thue-Morse sequences. A further construction, J. Number Theory, to appear. Zbl0916.11047
- [Sa] A. Sárközy, On the number of prime factors of integers of the form , Studia Sci. Math. Hungar. 23 (1988), 161-168.
- [Sc] A. Schinzel, Remarks on the paper 'Sur certaines hypothèses concernant les nombres premiers', Acta Arith. 7 (1961/1962), 1-8.
- [ScSi] A. Schinzel et W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arith. 4 (1958), 185-208; Corrigendum: Acta Arith. 5 (1959), 259.
- [St1] G. Stepanauskas, The mean values of multiplicative functions, II, Liet. Mat. Rink. 37 (1997), 212-223 (in Russian).
- [St2] G. Stepanauskas, The mean values of multiplicative functions, III, in: Analytic and Probabilistic Methods in Number Theory, New Trends in Probability and Statistics, Vol. 4, A. Laurinčikas et al. (eds.), VSP BV, Utrecht, 1997, 371-387. Zbl0977.11043
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.