A-expansions of Drinfeld modular forms

JOURNAL OF NUMBER THEORY

卷:133

Article

Petrov, Aleksandar

关键词: Drinfeld modular forms;    Expansions of Drinfeld modular forms;   

DOI  :  10.1016/j.jnt.2012.12.012

来源: Elsevier

【 摘 要 】

Text. We introduce the notion of Drinfeld modular forms with A-expansions, where instead of the usual Fourier expansion in tn (t being the uniformizer at 'infinity'), parametrized by n is an element of N, we look at expansions in t(alpha), parametrized by alpha is an element of A = F-q[T]. We construct an infinite family of eigenforms with A-expansions. Drinfeld modular forms with A-expansions have many desirable properties that allow us to explicitly compute the Hecke action. The applications of our results include; (i) various congruences between Drinfeld eigenforms; (ii) the computation of the eigensystems of Drinfeld modular forms with A-expansions; (iii) examples of failure of multiplicity one result, as well as a restrictive multiplicity one result for Drinfeld modular forms with A-expansions; (iv) examples of eigenforms that can be represented as 'non-trivial' products of eigenforms; (v) an extension of a result of Bock le and Pink concerning the Hecke properties of the space of cuspidal modulo double-cuspidal forms for Gamma(1)(T) to the groups GL(2)(F-q[T]) and Gamma(0)(T) Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=GCE_rN0gI9I. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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