Heights and totally real numbers

Real Hilbertianity and the Field of Totally Real Numbers

We use moduli spaces for covers of the Riemann sphere to solve regular embedding problems, with prescribed extendability of orderings, over PRC fields. As a corollary we show that the elementary theory of Qtr is decidable. Since the ring of integers of Qtr is undecidable, this gives a natural undecidable ring whose quotient field is decidable.

On the Product of Heights of Algebraic Numbers Summing to Real Numbers

Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

Sums of heights of algebraic numbers

For At(x) = f(x) − t g(x), we consider the set { ∑ At(α)=0 h(α) : t ∈ Q}. The polynomials f(x), g(x) are in Z[x], with only mild restrictions, and h(α) is the Weil height of α. We show that this set is dense in [d,∞) for some effectively computable limit point d.

Totally Real Representations and Real Function Spaces

Let G be a locally compact group. The notion of "totally real" unitary representation of G is defined and investigated in §1. In particular, if K is a compact subgroup of G, it is shown that every closed G-invariant subspace of L2(G/K) is spanned by real-valued functions if, and only if, KgK=Kg~K for every geG. In §2 the coset space X=G/K is specialized to a Riemannian symmetric space, where th...