Growth properties of the modular function j
type: Item
instance of: scholarly article
title: Growth properties of the modular function j
zbMATH Open document ID: 0678.10019
DOI: 10.1016/0022-247X(89)90115-7
author: Guy Diaz
author: Georges Philibert
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let j be the absolute invariant in the theory of modular functions. Theorem: For \(y\geq 1/2\), the function \(x\mapsto | j(x+iy)|\) increases for -1/2\(\leq x\leq 0\) and decreases for \(0\leq x\leq 1/2\). For - 1/2\(\leq x\leq 1/2\), the function \(y\mapsto | j(x+iy)|\) increases for \(y\geq (1-x^ 2)^{1/2}.\) [Reviewer's remark: The proofs of Propositions 2 and 3 can be simplified considerably.]
reviewed by: Günter Köhler
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 4110786
zbMATH Keywords: modular invariant growth
MaRDI profile type: Publication
cites work: Q4179073
cites work: Q4075566
cites work: On the coefficients of transformation polynomials for the modular function
cites work: Elliptic functions and transcendence
cites work: Q4154652
description: scientific article; zbMATH DE number 4110786