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Full-Text Articles in Mathematics
Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky
Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky
CMC Faculty Publications and Research
In his 1999 paper D. W. Masser talks about effective search bounds for polynomial equations over integers and rationals. This discussion can also be extended over number fields. Unfortunately, as illustrated by Matiasevich's negative answer to Hilbert's 10-th problem, search bounds in general probably do not exist. Some special cases are understood, but in general very little is known. I will talk about effective search bounds for solutions of polynomial equations over Q-bar with some additional arithmetic conditions. This discussion also naturaly ties into the realm of "absolute" diophantine results, like Siegel's lemma of Roy and Thunder. I will try …
Counting Lattice Points In Admissible Adelic Sets, Lenny Fukshansky
Counting Lattice Points In Admissible Adelic Sets, Lenny Fukshansky
CMC Faculty Publications and Research
Lecture given at the Midwest Number Theory Conference for Graduate Students and Recent PhDs II, February 2005.
Problems From The Cottonwood Room, Matthias Beck, Beifang Chen, Lenny Fukshansky, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, Achill Schürmann
Problems From The Cottonwood Room, Matthias Beck, Beifang Chen, Lenny Fukshansky, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, Achill Schürmann
CMC Faculty Publications and Research
This collection was compiled by Christian Haase and Bruce Reznick from problems presented at the problem sessions, and submissions solicited from the participants of the AMS/IMS/SIAM summer Research Conference on Integer points in polyhedra. Lattice points in homogeneously expanding compact domains. Presented by Lenny Fukshansky (Texas A&M University).