Journal of the Ramanujan Mathematical Society

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On A Product Expansion for the Drinfeld Discriminant Function


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1 Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
     

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The classical discriminant function Δ (τ) has a product expansion

Δ(τ) = (2πi)12qπ(1-qn)24,

where q = e2πiτ. E.-U. Gekeler gave in [4] a product expansion for the Drinfeld discriminant function of rank 2. In this paper, we give a product expansion for the Drinfeld discriminant function of arbitrary rank.


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  • On A Product Expansion for the Drinfeld Discriminant Function

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Authors

Yoshinori Hamahata
Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

Abstract


The classical discriminant function Δ (τ) has a product expansion

Δ(τ) = (2πi)12qπ(1-qn)24,

where q = e2πiτ. E.-U. Gekeler gave in [4] a product expansion for the Drinfeld discriminant function of rank 2. In this paper, we give a product expansion for the Drinfeld discriminant function of arbitrary rank.