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arXiv · 1310.1633

On hyperderivatives of single-cuspidal Drinfeld modular forms with A-expansions

Aleksandar Petrov
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Abstract

We show that the Drinfeld modular forms with $A$-expansion that have been constructed by the author are precisely the hyperderivatives of the subfamily of single-cuspidal Drinfeld modular forms with $A$-expansions that remain modular after hyperdifferentiation. In addition, we show that Drinfeld-Poincaré series display a similar behavior with respect to hyperdifferentiation, giving indirect evidence that the Drinfeld modular forms with $A$-expansions are Drinfeld-Poincaré series. The Drinfeld-Poincaré series that we consider generalize previous examples of such series by Gekeler, and Gerritzen and van der Put.

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Aleksandar Petrov. 2014-09-28. On hyperderivatives of single-cuspidal Drinfeld modular forms with A-expansions. https://arxiv.org/abs/1310.1633

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