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.
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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.
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Bassa, A., Beelen, P. A closed-form expression for the Drinfeld modular polynomial Φ T (X, Y). Arch. Math. 99, 237–245 (2012). https://doi.org/10.1007/s00013-012-0423-x
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DOI: https://doi.org/10.1007/s00013-012-0423-x