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1. with M. Jarden, σ-fields, PJM 185 (1998) 307–313. H(ilbert)'s I(rreducibility) T(heorem) is a diophantine limitation statement that applies to any number field. A field K satisfies HIT if for any finite collection of nonconstant maps (of degree at least 2) from algebraic curves, some values of K aren't in the image of any K points under these maps. The paper's main examples are g-Hilbertian fields. Such a field K is not the union of maps (at least degree 2) of K points from curves of genus at most g, yet there are g' > g for which this statement fails. Pending as of October 16, 2007. sigmahilb.html %-%-% sigmahilb.pdf

2. The Domain for Hilbert's Irreducibility Theorem, This file leads to a discussion of many aspects of Hilbert's Theorem, the most general arithmetic result on specializing algebraic objects to particular cases. Classical Domain Subtopics: Its application to the Inverse Galois Problem, producing high rank elliptic curves over Q; using Siegel's Thm. for precise HIT results; Universal Hilbert Subsets; Serre's Open Image Theorem as an HIT archetype. General Diophantine domain Subtopics: Weissauer's Thm. and relation between HIT and other arithmetic field properties; and the use of Pseudo-Algebraically-Closed fields to investigate the absolute Galois group of Q. HIT-domain.html

3. with S. R. Valluri (West. Ont. Univ.), Chebychev Derived Spindown Parameters for Gravitational Wave Signals from Pulsars, Canadian J. Physics Vol. 86 2008. 597–600. As of 10/10/07, noone has yet detected gravity waves, though General Relativity has predicted them for 80 years. Their most likely identifiable source is spinning neutron stars – weighty, yet tinier than the earth, stellar objects – by integrating space-perturbating data over long periods (several months at least). Such integration must cancel inter-solar-system data, and account for the neutron spin slowing with time. Neutron stars are a final stage for solar masses between standard red-giants and black holes. Inserting into the master equations parameters to detect what is involved in their spin-down is the topic of this paper. April3CJPFriedValluri.pdf

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