Paul Fili, Clayton Petsche, Igor Pritsker
Published 2015-07-07Version 1
We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy minimization problems with respect to the chordal metric on the projective line, and as an application, we obtain lower bounds on the Arakelov height in fields of totally real and totally p-adic numbers.
Energy integrals over local fields and global height bounds
Local heights on Galois covers of the projective line
On some notions of good reduction for endomorphisms of the projective line
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