On finite pseudorandom binary sequences III: The Liouville function, I

• Autorzy: Julien Cassaigne , Sébastien Ferenczi , Christian Mauduit , Jöel Rivat , András Sárközy
• Języki publikacji: EN

Kategorie tematyczne

• 11K45: Pseudo-random numbers; Monte Carlo methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 4
• Strony: 367-390

Daty

wydano

1999

otrzymano

1998-07-31

Twórcy

autor

Julien Cassaigne

• Institut de Mathématiques de Luminy, CNRS-UPR 9016, 163 av. de Luminy, Case 930, 13288 Marseille Cedex 9, France

autor

Sébastien Ferenczi

• Institut de Mathématiques de Luminy, CNRS-UPR 9016, 163 av. de Luminy, Case 930, 13288 Marseille Cedex 9, France

autor

Christian Mauduit

• Institut de Mathématiques de Luminy, CNRS-UPR 9016, 163 av. de Luminy, Case 930, 13288 Marseille Cedex 9, France

autor

Jöel Rivat

• Département de Mathématiques, Institut Girard Desargues, UPRES-A 5028, Université Claude Bernard, Lyon 1, 43, Bd du 11 Novembre 1918, Bât. 101, 69622 Villeurbanne Cedex, France

autor

András Sárközy

• Department of Algebra and Number Theory, Eötvös Loránd University, Múzeum krt. 6-8, 1088 Budapest, Hungary

Bibliografia

• [Ch] S. Chowla, The Riemann Hypothesis and Hilbert's Tenth Problem, Gordon and Breach, New York, 1965.
• [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.
• [HR] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974.
• [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.
• [Hi1] A. Hildebrand, Multiplicative functions at consecutive integers, Math. Proc. Cambridge Philos. Soc. 100 (1986), 229-236.
• [Hi2] A. Hildebrand, On consecutive values of the Liouville function, Enseign. Math. 32 (1986), 219-226.
• [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.
• [MS1] C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365-377.
• [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.
• [Sa] A. Sárközy, On the number of prime factors of integers of the form $a_i + b_j$, 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.