Spectra of Heights over Finite Groups.
by
Greg Dresden
Washington & Lee University

The (Weil) height of an algebraic number, h(\alpha), is related to the Mahler measure of its minimal polynomial p_\alpha(x) as follows: h(\alpha) = \frac1degp_\alphalogM(p_\alpha). While h(\alpha) is clearly dense in [0, \infty) as \alpha ranges over all algebraic numbers, Zhang showed that h(\alpha) + h(1-\alpha) is (at first) discrete. We expand this to other sums of heights of algebraic numbers, taking advantage of the group structure and of C. Smyth's recent work on discreteness and density of h(\alpha) for \alpha totally real.

http://www.wlu.edu/~dresdeng/

Date received: March 21, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-04.