Data di Pubblicazione:
2020
Citazione:
Greedy approximations by signed harmonic sums and the Thue–Morse sequence / S. Bettin, G. Molteni, C. Sanna. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 366(2020 Jun 03).
Abstract:
Given a real number τ, we study the approximation of τ by signed harmonic sums σN(τ):=∑n≤Nsn(τ)/n, where the sequence of signs (sN(τ))N∈N is defined “greedily” by setting sN+1(τ):=+1 if σN(τ)≤τ, and sN+1(τ):=−1 otherwise. More precisely, we compute the limit points and the decay rate of the sequence (σN(τ)−τ)N∈N. Moreover, we give an accurate description of the behavior of the sequence of signs (sN(τ))N∈N, highlighting a surprising connection with the Thue–Morse sequence.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Diophantine approximation; Egyptian fractions; Greedy algorithms
Elenco autori:
S. Bettin, G. Molteni, C. Sanna
Link alla scheda completa: