A conjectural extension of the Gross-Zagier formula on singular moduli
type: Item
instance of: scholarly article
title: A conjectural extension of the Gross-Zagier formula on singular moduli
zbMATH Open document ID: 0918.11032
author: Tim Hutchinson
published in: Tokyo Journal of Mathematics
publication date: 1999-08-23T00:00:00Z
review text: The formula in the title is for the resultant \(J(d_1,d_2)\) of the class polynomials for the orders of discriminant \(d_1,d_2\) of relatively prime fundamental discriminants of imaginary quadratics, due to \textit{B. H. Gross} and \textit{D. B. Zagier} [J. Reine Angew. Math. 355, 191-220 (1985; Zbl 0545.10015)]. The formula is interesting because it presents a highly composite resultant with factors \(F(m)\) equal to powers of primes of dividing \(m\) as \(m\) runs over positive integers \((d_1d_2-x^2)/4\). The author has conjectural extensions for the cases where \(d_1,d_2\) need not be fundamental and may have \((d_1,d_2)\) a prime power. There is an extended calculation serving as verification.
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 14K22
zbMATH DE Number: 1207098
zbMATH Keywords: complex multiplication
zbMATH Keywords: singular moduli
zbMATH Keywords: resultant of the class polynomials
zbMATH Keywords: orders
zbMATH Keywords: fundamental discriminants of imaginary quadratics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042000
OpenAlex ID: W1968993979
DOI: 10.3836/TJM/1270042000
description: scientific article; zbMATH DE number 1207098