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Heights and singular moduli of Drinfeld modules

Published 8 Mar 2023 in math.NT | (2303.04324v2)

Abstract: Let $q$ be an odd number and $q>5$, and $\mathbb{F}_q$ be a finite field of $q$ elements. We prove that at most finitely many singular moduli of rank 2 $\mathbb{F}_q[t]$-Drinfeld modules are algebraic units. In particular, we develop some techniques of heights of Drinfeld modules to approach it.

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