-distance sets, Falconer conjecture, and discrete analogs.
Kakutani-von Neumann maps on simplexes
Kapazität und Dimension verallgemeinerter Cantorscher Mengen
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
Khintchine types of translated coordinate hyperplanes
There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes, decidedly flat manifolds. In our main results, we fix the value of one coordinate in Euclidean space and describe the set of points in the fiber over that fixed coordinate that are rationally approximable at a given rate. We identify translated coordinate hyperplanes...
Khintchine-type theorems on manifolds
Kloosterman sums in residue classes
We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers
Kriterien in der Theorie der Gleichverteilung.
Kronecker-type sequences and nonarchimedean diophantine approximations