Abstract
A first encounter with \(A(\lambda):= \int_0^{+\infty} \{t\}\{\lambda t\} \frac{dt}{t^2}, \lambda > 0\), a continuous function with a strict local maximum at every rational point.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Alcántara-Bode, “Some properties of the Beurling function,” Pro Mathematica 14(27–28) (2000), 5–11.
L. Báez-Duarte, “A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis,” Rend. Mat. Ac. Lincei, S. 9, 14 (2003) 1, 5–11.
L. Báez-Duarte, M. Balazard, B. Landreau, et E. Saias, Notes sur la fonction ζ de Riemann, 3, Adv. in Math. 149 (2000), 130–144.
L. Báez-Duarte, M. Balazard, B. Landreau, et E. Saias, Sur l’autocorrélation multiplicative de la fonction partie fractionnaire, arXiv : math.NT/0306251.
A. Beurling, “A closure problem related to the Riemann Zeta-function,” Proc. Nat. Acad. Sci. 41 (1955), 312–314.
S. Chowla, and A. Walfisz, “Über eine Riemannsche Identität,” Acta Arith. 1 (1936), 87–112.
R. de la Bretèche, G. Tenenbaum, “Séries trigonométriques à coefficients arithmétiques,” Journal d’Analyse Mathématique 92 (2004), 1–79.
T. Estermann, “On the representation of a number as the sum of two products,” Proc. London Math. Soc. 31(2) (1930), 123–133.
M. Ishibashi, “The value of the Estermann zeta functions at s = 0,” Acta Arith. 73 (1995), 357–361.
M. Jutila, “Lectures on a method in the theory of exponential sums,” TIFR Lectures on Mathematics and Physics, Springer-Verlag, Berlin, 1987.
D. H. Lehmer, “Euler constants for arithmetical progressions,” Acta Arith. 27 (1975), 125–142.
B. Nyman, “On some groups and semigroups of translations,” Thèse, Uppsala, 1950.
J. J. Sylvester, “Sur la fonction E(x),” C. R. A. S. 50 (1860), 732–734.
V. I. Vassiounine, “Sur un système biorthogonal relié à l’hypothèse de Riemann (en russe),” Alg. i An. 7 (1995), 118–135; traduction anglaise dans St-Petersburg Math. J. 7 (1996), 405–419.
A. Walfisz, “Über einige trigonometrische Summen,” Math. Z. 33 (1931), 564–601.
A. Zygmund, Trigonometric Series, 2nd ed. Vols. I, II., Cambridge University Press, New York, 1959.
Author information
Authors and Affiliations
Corresponding author
Additional information
Pour Jean-Louis Nicolas, avec affection
2000 Mathematics Subject Classification: Primary—11M26, 11M41
Rights and permissions
About this article
Cite this article
Báez-Duarte, L., Balazard, M., Landreau, B. et al. Étude de l’autocorrélation multiplicative de la fonction ‘partie fractionnaire’. Ramanujan J 9, 215–240 (2005). https://doi.org/10.1007/s11139-005-0834-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-005-0834-4