The present paper deals with Atkin–Lehner theory for Drinfeld modular forms. We provide an equivalent definition of 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 exhibit p-newforms arising from lower levels and we provide p-adic Drinfeld modular forms of level greater than 1.

Atkin–Lehner theory for Drinfeld modular forms and applications

Valentino M.
2022-01-01

Abstract

The present paper deals with Atkin–Lehner theory for Drinfeld modular forms. We provide an equivalent definition of 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 exhibit p-newforms arising from lower levels and we provide p-adic Drinfeld modular forms of level greater than 1.
Atkin–Lehner involutions
Drinfeld modular forms
p-Adic modular forms
p-Newforms
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/341938
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