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arXiv · 2012.08480

Atkin-Lehner theory for Drinfeld modular forms and applications

Maria Valentino
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Abstract

The present paper deals with Atkin-Lehner theory for Drinfeld modular forms. We provide an equivalent definition of $\mathfrak{p}$-newforms (which makes computations easier) and commutativity results between Hecke operators and Atkin-Lehner involutions. As applications we show a criterion for a direct sum decomposition of cusp forms, we exibit $\mathfrak{p}$-newforms arising from lower levels and we provide $\mathfrak{p}$-adic Drinfeld modular forms of level greater than 1.

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Maria Valentino. 2020-12-15. Atkin-Lehner theory for Drinfeld modular forms and applications. https://arxiv.org/abs/2012.08480

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