Category
Algebraic number theory
Related publications (38)
Multiplicative combinatorial properties of return time sets in minimal dynamical systems
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove t ...
2019The Bounded Cohomology of SL2 Over Local Fields and S-Integers
It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...
OXFORD UNIV PRESS2019Forbidden induced subposets of given height
Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2019Lonely Runner Polyhedra
We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...
2018Almost tiling of the Boolean lattice with copies of a poset
Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...
ELECTRONIC JOURNAL OF COMBINATORICS2018Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients
For any positive integers we present formulae for the number of irreducible polynomials of degree over the finite field where the coefficients of , and are zero. Our proofs involve coun ...
Elsevier2016CM values of higher Green's functions and regularized Petersson products
Higher Green functions are real-valued functions of two variables on the upper half-plane, which are bi-invariant under the action of a congruence subgroup, have a logarithmic singularity along the diagonal, and satisfy the equation f = k(1−k) f ; here i ...
Cambridge UP2015Cross-Intersecting Families of Vectors
Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...
Springer Japan Kk2015Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex
We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant such that whenever are n-element subsets of , we can find a point and subsets for every , each of size at least , suc ...
Springer2015An extremal problem on crossing vectors
Bartosz Maria Walczak, Michal Lason
For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] - A[j] >= k. What is the maximum size of a family of pairwise 1-crossing and pairwise non-k-crossing ...
Academic Press Inc Elsevier Science2014