4 papers
Separated sets and the Falconer conjecture for polygonal norms
Sergei Konyagin, Izabella Laba
The Falconer conjecture asserts that if E is a planar set with Hausdorff dimension strictly greater than 1, then its Euclidean distance set has positive one-dimensional Lebesgue me…
Distance sets of well-distributed planar sets for polygonal norms
Sergei Konyagin, Izabella Laba
Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX must be if X contains a well-distribu…
Rearrangements of Trigonometric Series and Trigonometric Polynomials
S. V. Konyagin
The paper is related to the following question of P.~L.~Ul'yanov: is it true that for any -periodic continuous function there is a uniformly convergent rearrangement of its…
Enumerating Permutation Polynomials over finite fields by degree
Sergei Konyagin, Francesco Pappalardi
We prove an asymptotic formula for the number of permutation for which the associated permutation polynomial has degree smaller than .