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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…
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…
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…
Bad() is hyperplane absolute winning
Victor Beresnevich, Erez Nesharim, Lei Yang
In 1998 Kleinbock conjectured that any set of weighted badly approximable real matrices is a winning subset in the sense of Schmidt's game. In this paper we prove this…
Winning property of badly approximable points on curves
Victor Beresnevich, Erez Nesharim, Lei Yang
In this paper we prove that badly approximable points on any analytic non-degenerate curve in is an absolute winning set. This confirms a key conjecture in the area…
Metric Diophantine approximation with congruence conditions
Erez Nesharim, Rene Rühr, Ronggang Shi
We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani corre…