Coefficients of Drinfeld modular forms and Hecke operators

JOURNAL OF NUMBER THEORY

卷:131

Article

Armana, Cecile

关键词: Drinfeld modular forms;    Hecke operators;   

DOI  :  10.1016/j.jnt.2011.02.011

来源: Elsevier

【 摘 要 】

Consider the space of Drinfeld modular forms of fixed weight and type for Gamma(0)(n) subset of GL(2)(Fq[T]). It has a linear form N. given by the coefficient of t(m+n(q-1)) in the power series expansion of a type m modular form at the cusp infinity, with respect to the uniformizer t. It also has an action of a Hecke algebra. Our aim is to study the Hecke module spanned by N. We give elements in the Hecke annihilator of b(1). Some of them are expected to be nontrivial and such a phenomenon does not occur for classical modular forms. Moreover, we show that the Hecke module considered is spanned by coefficients b(n), where n runs through an infinite set of integers. As a consequence, for any Drinfeld Hecke eigenform, we can compute explicitly certain coefficients in terms of the eigenvalues. We give an application to coefficients of the Drinfeld Hecke eigenform h. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free