Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

Abstract

We find a generator $j_{1,4}$ of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator $N(j_{1,4})$ which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.