On the Atkin 𝑈_{𝑡}-operator for Γ₀(𝑡)-invariant Drinfeld cusp forms

Bandini, Andrea; Valentino, Maria

doi:10.1090/proc/14491

On the Atkin $U_t$-operator for $\Gamma _0(t)$-invariant Drinfeld cusp forms
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by Andrea Bandini and Maria Valentino PDF

Proc. Amer. Math. Soc. 147 (2019), 4171-4187 Request permission

Abstract:

We study the Atkin $U_t$ operator for Drinfeld cusp forms. In particular, we define newforms and oldforms of level $\Gamma _0(t)$ and we study basic properties of their slopes. Moreover, we find an explicit formula for the matrix associated to the action of $U_t$ on $\Gamma _1(t)$-invariant cusp forms using Teitelbaum’s interpretation as harmonic cocycles.

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