TY - CONF

T1 - Sur la répartition jointe de la représentation d’Ostrowski dans les classes de résidus

AU - Amri, Myriam

PY - 2020/11/19

Y1 - 2020/11/19

N2 - 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).

AB - 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).

M3 - Presentation

T2 - Séminaire de théorie des nombres (Nancy-Metz)

Y2 - 19 August 2021

ER -