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arXiv · 2509.20895

A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank

Oğuz Gezmiş·Özge Ülkem
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Abstract

We aim to provide an infinite family of cuspidal Drinfeld-Hecke eigenforms given in terms of a determinant of twisted Eisenstein series. Our main tool is the theory of vectorial Drinfeld modular forms, previously introduced by Pellarin [20] and extensively studied by Pellarin [21] as well as in his joint work with Perkins [22] in the rank two setting. We will develop this theory in the present paper for the arbitrary rank setting by using a particular representation.

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Oğuz Gezmiş, Özge Ülkem. 2025-09-25. A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank. https://arxiv.org/abs/2509.20895

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