On the coefficients of transformation polynomials for the modular function
- 17 April 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 10 (2) , 197-218
- https://doi.org/10.1017/s0004972700040831
Abstract
In a previous paper (Acta Arith. 21 (1972), 89–97), I had proved that the sum of the absolute values of the coefficients of the mth transformation polynomial Fm (u, v) of the Weber modular function j(ω) of level 1 is not greater than 2(36n+57)2n when m = 2n is a power of 2. The aim of the present paper is to give an analogous bound for the case of general m. This upper bound is much less good and of the form where c > 0 is an absolute constant which can be determined effectively. It seems probable that also in the general case an upper bound of the form eO(m10gm) should hold, but I have not so far succeeded in proving such a result.Keywords
This publication has 3 references indexed in Scilit:
- On the coefficients of the $2^n$-th transformation polynomial for j(ω)Acta Arithmetica, 1972
- On Some Diophantine Inequalities Involving the Exponential FunctionCanadian Journal of Mathematics, 1965
- On Some Inequalities for Polynomials in Several VariablesJournal of the London Mathematical Society, 1962