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math.NT2026
Arboreal Galois representations of rational functions: fixed-point proportion and the extension problem
Jorge Fariña-Asategui
We give an explicit description of the arithmetic-geometric extension of iterated Galois groups of rational functions. This yields a complete solution to the extension problem when…
math.NT2026
Fixed-point proportion of geometric iterated Galois groups
Jorge Fariña-Asategui, Santiago Radi
In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal…