Generalized Mahler measures and equidistribution

speaker: Thomas Tucker (University of Rochester)

abstract: Mahler showed that the usual height of an algebraic number x with minimal polynomial F can computed by integrating log
F
along the unit circle. This has been generalized to a formula relating canonical heights attached to rational maps g to integrals of log
F
along invariant measures for g. A variety of authors have proven results say that families of points of small height are equidistributed with respect to these measures. It turns out that these do not extend completely to integrals involving the functions log
F
mentioned above. We will discuss what is know for the functions log
F
and how these questions relate to questions about differences between heights and adelic pairings between canonically metrized line bundles.

timetable:
Tue 12 Jul, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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