Sur la répartition jointe de la représentation d’Ostrowski dans les classes de résidus
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Abstract
For two distinct integers m1, m2 ≥ 2, we set α1 = [0; 1, m1] and α2 = [0; 1, m2]
(where [0; 1, m] is the continued fraction [0; 1, m, 1, m, 1, m, . . .]) and we let S_α1
(n) and S_α2(n) denote respectively, the sum of digits functions in the Ostrowski α1 and α2−representations of n. Let b1, b2 be positive integers satisfying (b1, m1) = 1 and (b2, m2) = 1, we obtain an estimation N/b1b2 with an error term O(N1−δ) for the cardinality of the following set
{ n, 0 ≤ n < N; S_α1(n) ≡ a1 (mod b1), S_α2(n) ≡ a2 (mod b2)}
for all integers a1 and a2.
Our result should be compared to that of Bésineau and Kim who addressed the case of the
q−representations in different bases (that are coprime).
Details
Translated title of the contribution | On the joint distribution of the Ostrowski representation in residue classes |
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Original language | French |
Publication status | Published - 19 Nov 2020 |
Event | Séminaire de théorie des nombres (Nancy-Metz) - Université de Loraine, Nancy, France Duration: 19 Aug 2021 → … https://iecl.univ-lorraine.fr/events/categories/analyse-et-theorie-des-nombres/seminaire-de-theorie-des-nombres-de-nancy-metz/ |
Seminar
Seminar | Séminaire de théorie des nombres (Nancy-Metz) |
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Country/Territory | France |
City | Nancy |
Period | 19/08/21 → … |
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