, Volume 99, Issue 3, pp 237-245

A closed-form expression for the Drinfeld modular polynomial Φ T (X, Y)

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Abstract

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

Peter Beelen gratefully acknowledges the support from the Danish National Research Foundation and the National Science Foundation of China (Grant No.11061130539) for the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography.