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Generalized Ramanujan-Sato Series Arising from Modular Forms
Angelica Babei, Lea Beneish, Manami Roy +3
Motivated by work of Chan, Chan, and Liu, we obtain a new general theorem which produces Ramanujan-Sato series for . We then use it to construct explicit examples related to n…
Stochastic Equidistribution and Generalized Adelic Measures
John Doyle, Paul Fili, Bella Tobin
We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field,…
Some Applications of Dynamical Belyi Polynomials
Jacqueline Anderson, Michelle Manes, Bella Tobin
We give necessary and sufficient conditions for post-critically finite polynomials to have persistent bad reduction at a given prime. We also answer in the negative a pair of quest…
Cubic post-critically finite polynomials defined over
Jacqueline Anderson, Michelle Manes, Bella Tobin
We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over , up to conjugacy over .…
Dessins d'Enfants for Single-Cycle Belyi Maps
Michelle Manes, Gabrielle Melamed, Bella Tobin
Riemann's Existence Theorem gives the following bijections: (1) Isomorphism classes of Belyi maps of degree . (2) Equivalence classes of generating systems of degree . (3) Is…