On K2 (...) and presentations of SLn (...) in the real quadratic case.
On K2 of Finite Dimensional Division Algebras Over Arithmetical Fields.
On Karatsuba Conjecture and the Lindelöf Hypothesis
On (..., k)-Normal Words in Connecting Dynamical Systems.
On knots in algebraic number theory.
On Krasner's Criteria for the First Case of Fermat's Last Theorem.
On Krasnér's theorem for the first case of Fermat's last theorem
On Kronecker équivalence of algebraic number fields.
On Kronecker's elimination theory.
On Kronecker's limit formula for Dirichlet series with periodic coefficients
On K-Stage Euclidean algorithms for Galois extensions of Q.
On k-triad sequences.
On Kurepa's problems in number theory.
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.
On large values of the Riemann zeta-function on short segments of the critical line
We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.
On lattice bases with special properties
In this paper we introduce multiplicative lattices in and determine finite unions of suitable simplices as fundamental domains for sublattices of finite index. For this we define cyclic non-negative bases in arbitrary lattices. These bases are then used to calculate Shintani cones in totally real algebraic number fields. We mainly concentrate our considerations to lattices in two and three dimensions corresponding to cubic and quartic fields.
On lattice points in large convex bodies
On Lattice Points in Polyhedral Cross-Sections.
On lattice polytopes having interior lattice points.