12 citations · 38 across the 14 of their papers we have counts for
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math.NT2017★ 10 cited
Gonality of dynatomic curves and strong uniform boundedness of preperiodic points
John R. Doyle, Bjorn Poonen
Fix and a field such that . Assume that contains the th roots of . Then the irreducible components of the curves over parameter…
math.DS2017
Dynamical modular curves for quadratic polynomial maps
John R. Doyle
Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain cla…
math.DS2017★ 5 cited
Reduction of dynatomic curves
John R. Doyle, Holly Krieger, Andrew Obus +3
The dynatomic modular curves parametrize polynomial maps together with a point of period . It is known that the dynatomic curves are smooth and irreducible in character…