LOWER BOUNDS FOR THE CANONICAL HEIGHT ON DRINFELD MODULES

Vincent Bosser (1) , Aurélien Galateau (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We use diophantine approximation to bound from below the canon-ical height on a Drinfeld module. We first give a positive answer to the Lehmer problem in the case of purely inseparable extensions on Drinfeld modules with at least one supersingular prime. We also revisit the CM case, where we improve the estimates already known, and we finally give a bound of polynomial strength in the general case.

Domains: Mathematics [math]; Number Theory [math.NT]

Vincent Bosser, Aurélien Galateau. LOWER BOUNDS FOR THE CANONICAL HEIGHT ON DRINFELD MODULES. International Mathematics Research Notices, 2019, 2019 (1), pp.165-200. ⟨10.1093/imrn/rnx112⟩. ⟨hal-02151916⟩