On a problem of Hasse and Ramachandra

Abstract

Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when 𝔣 = (N) for any positive integer N excluding 2, 3, 4 and 6.

Keywords

• class field theory
• complex multiplication
• weber function
• primary 11r37
• secondary 11g15
• 11g16