Elisa Bellah

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math.NT2025

Connectedness of special points in the Markoff mod $p$ graphs

Elisa Bellah, Claire Dunn, Vernon Naidu +1

It is conjectured that the Markoff equation $X^{2} + Y^{2} + Z^{2} = 3 X Y Z$ satisfies the special Diophantine property that every mod $p$ solution lifts to an integer solution. Progress toward…

math.NT2023

Bounding Lifts of Markoff Triples mod $p$

Elisa Bellah, Siran Chen, Elena Fuchs +1

In 2016, Bourgain, Gamburd, and Sarnak proved that Strong Approximation holds for the Markoff surface in most cases. That is, the modulo $p$ solutions to the equation $X_1^2+X_2^2+…

Connectedness of special points in the Markoff mod p graphs

Bounding Lifts of Markoff Triples mod p

Connectedness of special points in the Markoff mod $p$ graphs

Bounding Lifts of Markoff Triples mod $p$