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Arithmetic unlikely intersections in powers of the multiplicative group
Francesco Campagna, Gabriel Andreas Dill, Robert Wilms
Inspired by work of Bugeaud-Corvaja-Zannier, we formulate a conjecture about unlikely intersections in powers of the multiplicative group over the ring of integers in a number fiel…
Ordinary isogeny graphs over : the inverse volcano problem
Henry Bambury, Francesco Campagna, Fabien Pazuki
We give a detailed presentation of -isogeny graphs associated with ordinary elliptic curves defined over . We then focus on the following inverse problem: given…
Around the support problem for Hilbert class polynomials
Francesco Campagna, Gabriel Andreas Dill
Let denote the Hilbert class polynomial of the imaginary quadratic order of discriminant . We study the rate of growth of the greatest common divisor of and $H…
On singular moduli that are S-units
Francesco Campagna
Recently Yu. Bilu, P. Habegger and L. Kühne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime number…