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- W2056525811 abstract "We introduce the notion of Drinfeld modular forms with $A$-expansions, where instead of the usual Fourier expansion in $t^n$ ($t$ being the uniformizer at `infinity'), parametrized by $n in mathbb{N}$, we look at expansions in $t_a$, parametrized by $a in A = Fq [T]$. 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 B{o}ckle and Pink concerning the Hecke properties of the space of cuspidal modulo double-cuspidal forms for $Gamma_1(T)$ to the groups $text{GL}_2 (Fq [T])$ and $Gamma_0(T)$." @default.
- W2056525811 created "2016-06-24" @default.
- W2056525811 creator A5046157349 @default.
- W2056525811 date "2013-07-01" @default.
- W2056525811 modified "2023-09-27" @default.
- W2056525811 title "A -expansions of Drinfeld modular forms" @default.
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- W2056525811 doi "https://doi.org/10.1016/j.jnt.2012.12.012" @default.
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