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Dynamics on algebraic surfaces MPI Arbeitstagung 2007
 

Summary: Dynamics on algebraic surfaces
MPI Arbeitstagung 2007
Curtis T. McMullen
In this talk we discuss connections between algebraic integers and auto-
morphisms of compact complex surfaces.
Integers. Conjecturally, the smallest algebraic integer > 1 is the root
Lehmer = 1.1762808 . . . of Lehmer's polynomial,
P(x) = 1 + x - x3
- x4
- x5
- x6
- x7
+ x9
+ x10
.
By smallest we mean the Mahler measure, given by the product of the
conjugates of outside the unit disk, is minimized. In fact Lehmer is a
Salem number: it is the unique root of P(x) outside the disk, so it is its own
Mahler measure.
Lehmer's polynomial has several geometric manifestations; especially, it

  

Source: McMullen, Curtis T.- Department of Mathematics, Harvard University

 

Collections: Mathematics