Entire or rational maps with integer multipliers - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Entire or rational maps with integer multipliers

Résumé

Let OK be the ring of integers of an imaginary quadratic field K. Recently, Ji and Xie proved that every rational map f:ˆCˆC of degree d2 whose multipliers all lie in OK is a power map, a Chebyshev map or a Lattès map. Their proof relies on a result from non-Archimedean dynamics obtained by Rivera-Letelier. In the present note, we show that one can avoid using this result by considering a differential equation instead. Our proof of Ji and Xie's result also applies to the case of entire maps. Thus, we also show that every nonaffine entire map f:CC whose multipliers all lie in OK is a power map or a Chebyshev map.
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Dates et versions

hal-04854826 , version 1 (23-12-2024)

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Xavier Buff, Thomas Gauthier, Valentin Huguin, Jasmin Raissy. Entire or rational maps with integer multipliers. 2024. ⟨hal-04854826⟩
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