A closed form expression for the Drinfeld modular polynomial $Φ_T(X,Y)$

preprint2012arXivOpen access

In this paper we give a closed form expression for the Drinfeld modular polynomial $Φ_T(X,Y) \in \mathbb{F}_q(T)[X,Y]$ for arbitrary $q$ and prove a conjecture of Schweizer. A new identity involving the Catalan numbers plays a central role.

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A closed form expression for the Drinfeld modular polynomial $Φ_T(X,Y)$

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A closed form expression for the Drinfeld modular polynomial ΦT(X,Y)Φ_T(X,Y)ΦT​(X,Y)

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A closed form expression for the Drinfeld modular polynomial $Φ_T(X,Y)$