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math.NT2025
Sums of Laurent series with bounded partial quotients
Dmitry Gayfulin, Erez Nesharim
In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most . Later, Cusick proved that every real number is t…
math.NT2025
Every real number is a sum of two real numbers with diverging partial quotients
Dmitry Gayfulin, Erez Nesharim
We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which w…
math.NT2025
Escape of mass of the Thue-Morse sequence
Erez Nesharim, Uri Shapira, Noy Soffer Aranov
Every Laurent series in has a continued fraction expansion whose partial quotients are polynomials. De Mathan and Teulié proved that…