A non-standard Fourier expansion for the Drinfeld discriminant function
type: Item
instance of: scholarly article
title: A non-standard Fourier expansion for the Drinfeld discriminant function
zbMATH Open document ID: 1227.11068
author: Bartolomé López
published in: Archiv der Mathematik
publication date: 2010-09-08T00:00:00Z
review text: Let \(A={\mathbb F}_q[T]\), \(K={\mathbb F}_q(T)\), \(K_\infty={\mathbb F}_q\left(\left(\frac 1T\right)\right)\), \(C\) the completed algebraic closure of \(K_\infty\). The Carlitz module determines a rank one \(A\)-module in \(C\) generated by an element \(\overline{\pi}\). Let \(t(z)=\frac{1}{\overline{\pi}} \sum_{a\in A}\frac{1}{z+a}\). For the Drinfeld discriminant function \(\Delta(z)\) the author proves that \[ \overline{\pi}^{1-q^2}\Delta(z)=-\sum_{\substack{ a\in A\\ a\,\text{monic}}} a^{q(q-1)}t(az)^{q-1}. \]
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11F52
Mathematics Subject Classification ID: 11G09
zbMATH DE Number: 5781192
zbMATH Keywords: Drinfeld modular forms
MaRDI profile type: Publication
full work available at URL: s00013-010-0148-7
OpenAlex ID: W2087445044
cites work: On the coefficients of Drinfeld modular forms
DOI: 10.1007/S00013-010-0148-7
description: scientific article; zbMATH DE number 5781192