Paul Fili, Igor Pritsker
Published 2015-07-07Version 1
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.
Height bounds on zeros of quadratic forms over $\overline{\mathbb Q}$
Energy integrals over local fields and global height bounds
Arithmetic of hyperelliptic curves over local fields
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