Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772592 | Journal of Number Theory | 2017 | 13 Pages |
Abstract
In an earlier work, the first author and Petsche solved an energy minimization problem for local fields and used the result to obtain lower bounds on the height of algebraic numbers all whose conjugates lie in various local fields, such as totally real and totally p-adic numbers. In this paper, we extend these techniques and solve the corresponding minimization programs for real intervals and p-adic discs, obtaining several new lower bounds for the height of algebraic numbers all of whose conjugates lie in such sets.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Paul Fili, Igor Pritsker,