On the usual product of rational arithmetic functions

Let K denote a number field, S a finite set of places of K, and ϕ: ℙⁿ → ℙⁿ a rational morphism defined over K. The main result of this paper states that there are only finitely many twists of ϕ defined over K which have good reduction at all places outside S. This answers a question of Silverman in the affirmative.

Arithmetic functions on Beatty sequences

Abercrombie Alex G., Banks William D., Shparlinski Igor E. (2009)

Acta Arithmetica

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