Julia Robinson's Numbers
Pierre Gillibert, Gabriele Ranieri (Instituto de Matematica -, Pontificia Universidad Cat\'olica de Valpara\'iso)
TL;DR
This paper constructs an infinite family of algebraic integer rings in totally real subfields of Q with Julia Robinson's Numbers that are neither 4 nor infinite, and shows this set is unbounded.
Contribution
It introduces a new family of algebraic integer rings with distinct Julia Robinson's Numbers, expanding understanding of their possible values.
Findings
Constructed an infinite family of rings with Julia Robinson's Numbers not equal to 4 or infinity.
Showed the set of Julia Robinson's Numbers in this family is unbounded.
Partially answered a question by Vidaux and Videla.
Abstract
We partially answer to a question of Vidaux and Videla by constructing an infinite family of rings of algebraic integers of totally real subfields of Q whose Julia Robinson's Number is distinct from 4 and +. Moreover the set of the Julia Robinson's Number that we construct is unbounded.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Limits and Structures in Graph Theory