Arithmetic of Eisenstein series of level T for the function field modular group

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• 作者：Enrico Varela Roldá ; n ^{varela@math.uni-sb.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11F52
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：167
• 期：Complete
• 页码：180-201
• 全文大小：388 K

文摘

In this paper we study the structure of the algebra of Drinfeld modular forms for the principal congruence subgroup Γ(T)$\mathrm{\Gamma }(T)$ of the full modular group GL(2,F_q[T])$\mathrm{GL}(2,{\mathbb{F}}_q[T])$.

To this end and based on work of Cornelissen, we introduce a new class of Eisenstein series and describe their fundamental properties. These so-called modified Eisenstein series allow for a simplification of prior results and are an indispensable tool for future work on Drinfeld modular forms of level T.