Abstract
L’inégalité d’Erdös-Turán mesure l’écart à l’équirépartition d’une suite quelconque du tore en fonction d’un paramètre arbitraire et de deux constantes absolues, c1 et c2. Nous montrons que c1≥ 1 et c2≥ 2/π, et nous fournissons un ensemble de couples admissibles (c1;c2) numériquement proches de l’optimum hypothétique (1;2/π), notamment (1;0,653) et (1,1435;2/π).
The Erdös-Turán inequality measures the distance from uniform distribution of any given sequence on the torus as a function of an arbitrary parameter and two constants, c1 and c2. We show that c1≥ 1 and c2≥ 2/π, and we provide a set of admissible pairs (c1;c2) that are numerically close to the hypothetical optimum (1;2/π), including (1;0.653) and (1.1435;2/π).
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References
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À Jean-Louis Nicolas, avec toute notre amitié
2000 Mathematics Subject Classification: Primary—11K38, 11K06; Secondary—11L03, 42A05
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Rivat, J., Tenenbaum, G. Constantes d’Erdös–Turán. Ramanujan J 9, 111–121 (2005). https://doi.org/10.1007/s11139-005-0829-1
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DOI: https://doi.org/10.1007/s11139-005-0829-1