3,187 research outputs found
Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers
We prove decidability of univariate real algebra extended with predicates for
rational and integer powers, i.e., and . Our decision procedure combines computation over real algebraic
cells with the rational root theorem and witness construction via algebraic
number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated
Deduction, 2015. Proceedings to be published by Springer-Verla
Integer Points in Backward Orbits
A theorem of J. Silverman states that a forward orbit of a rational map
on contains finitely many -integers in the number
field when is not a polynomial. We state an analogous
conjecture for the backward orbits using a general -integrality notion based
on the Galois conjugates of points. This conjecture is proven for the map
, and consequently Chebyshev polynomials, by uniformly bounding
the number of Galois orbits for when is a non-root
of unity. In general, our conjecture is true provided that the number of Galois
orbits for is bounded independently of .Comment: 13 page
On the unification of quantum 3-manifold invariants
In 2006 Habiro initiated a construction of generating functions for
Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In
a series of papers together with Irmgard Buehler and Christian Blanchet we
extended his construction to a larger class of 3-manifolds. The unified
invariants provide a strong tool to study properties of the whole collection of
WRT invariants, e.g. their integrality, and hence, their categorification. In
this paper we give a survey on ideas and techniques used in the construction of
the unified invariants.Comment: 18 page
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