Universal counting of lattice points in polytopes.
Universal expansions in negative and complex bases.
Universal forms and Waring’s problem
Universal formulae of Euler-Fermat type for subsets of Zm.
Universal normal bases for the abelian closure of the field of rational numbers
Universal norms of -units in some non-commutative Galois extensions.
Universal sets and the vector game.
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups.
Universal tessellations.
All maps of type (m,n) are covered by a universal map M(m,n) which lies on one of the three simply connected Riemann surfaces; in fact M(m,n) covers all maps of type (r,s) where r|m and s|n. In this paper we construct a tessellation M which is universal for all maps on all surfaces. We also consider the tessellation M(8,3) which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3) and M.
Universality of a non-classical integral quadratic form over ℚ(√5)
Universality results on Hurwitz zeta-functions
In the paper, we give a survey of the results on the approximation of analytic functions by shifts of Hurwitz zeta-functions. Theorems of such a kind are called universality theorems. Continuous, discrete and joint universality theorems of Hurwitz zeta-functions are discussed.
Univoque numbers and an avatar of Thue-Morse
Univoque sets for real numbers
For x ∈ (0,1), the univoque set for x, denoted (x), is defined to be the set of β ∈ (1,2) such that x has only one representation of the form x = x₁/β + x₂/β² + ⋯ with . We prove that for any x ∈ (0,1), (x) contains a sequence increasing to 2. Moreover, (x) is a Lebesgue null set of Hausdorff dimension 1; both (x) and its closure are nowhere dense.
Unramified cohomology and rationality problems.
Unramified Kummer extensions of prime power degree.
Unramified quaternion extensions of quadratic number fields
Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields correspond to certain factorizations of its discriminant disc . In this paper we extend their results to unramified quaternion extensions of which are normal over , and show how to construct them explicitly.
Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic.
Unsolvability of the Pell minus-equation for certain odd discriminants
Untere Abschätzung für die Anzahl der B-Zwillinge auf kurzen Intervallen
Untere Schranken für den ersten Eigenwert des Laplace-Operators auf kompakten Riemannschen Flächen.