A new look at Jarvis' distribution formula
type: Item
instance of: scholarly article
title: A new look at Jarvis' distribution formula
zbMATH Open document ID: 1190.19003
published in: Journal of Number Theory
publication date: 2009-05-19T00:00:00Z
review text: In two papers [Bull. Lond. Math. Soc. 32, No. 2, 146--154 (2000; Zbl 1024.11042), Manuscr. Math. 103, No. 3, 329--337 (2000; Zbl 1024.11041)], \textit{F. Jarvis} proved that if \(L\) and \(\Lambda\) are lattices in \({\mathbb C}\), \(\psi: E = {\mathbb C}/L \to {\mathbb C}/\Lambda=F\) an isogeny between the corresponding elliptic curves, \(D\) a divisor satisfying certain conditions and \(\phi_{\Lambda}\), \(\phi_L\) the Siegel functions associated to the lattices \(\Lambda\) and \(L\) then the following distribution formula holds: \[ \phi_\Lambda(\psi(D)) = \prod_{S \in \ker(\psi)} \phi_L(D \oplus S) \] This result played an essential role in the construction of elements in the second \(K\)-group of an elliptic curve given by \textit{K. Rolshausen} and \textit{N. Schappacher} in [J. Reine Angew. Math. 495, 61--77 (1998; Zbl 0887.11027)]. In the paper under review the author gives a proof of a general distribution formula for Siegel functions of divisors on \({\mathbb C}\) which implies Jarvis' result when one descends to elliptic curves. The main ingredient in the proof is the distribution formula for Klein functions.
reviewed by: Keith Johnson
Mathematics Subject Classification ID: 19F15
Mathematics Subject Classification ID: 19F27
Mathematics Subject Classification ID: 11G16
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 5554699
zbMATH Keywords: Siegel functions
zbMATH Keywords: Klein functions
zbMATH Keywords: distribution formula
zbMATH Keywords: elliptic curves
zbMATH Keywords: algebraic K-theory
author: Eugenio Jesús Gómez Ayala
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.02.002
OpenAlex ID: W2054550783
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DOI: 10.1016/J.JNT.2009.02.002
description: scientific article; zbMATH DE number 5554699