Growth properties of the modular function j
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.]
scientific article; zbMATH DE number 4110786