10 citations · 24 across the 8 of their papers we have counts for
12 papers
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…
Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images
Ábel Farkas, Jonathan M. Fraser, Erez Nesharim +1
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supre…
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…
On the -adic Littlewood Conjecture
Faustin Adiceam, Erez Nesharim, Fred Lunnon
The -adic Littlewood Conjecture due to De Mathan and Teulié asserts that for any prime number and any real number , the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\l…
Schmidt games and Cantor winning sets
Dzmitry Badziahin, Stephen Harrap, Erez Nesharim +1
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and ap…
Solution of Cassels' Problem on a Diophantine Constant over Function Fields
Efrat Bank, Erez Nesharim, Steffen Højris Pedersen
This paper deals with the analogue of Inhomogeneous Diophantine Approximation in function fields. The inhomogeneous approximation constant of a Laurent series $θ\in\mathbb F_q\left…
is hyperplane absolute winning
Erez Nesharim, David S. Simmons
J. An (2013) proved that for any such that , is -winning for Schmidt's game. We show that using the main lemma from An…
Badly approximable vectors on a vertical Cantor set
Erez Nesharim
For , the set of badly approximable vectors with weight is defined by $Bad(i, j) = \{(x, y) \in \R^2 : \exists c > 0 \forall q\in\N, \;\; \max\{q||qx|…