On a problem of Hasse and Ramachandra

2016/08/24 by Koo, Ja Kyung, Shin, Dong Hwa, Yoon, Dong Sung
#11G15 #11G16 (Secondary) #11R37 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.06705

Abstract

Let K be an imaginary quadratic field, and let \mathfrakf be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo \mathfrakf can be generated by a single value of the Weber function. We completely resolve this question when \mathfrakf=(N) for an integer N>1.

Related

• Generation of class fields by using the Weber function
• Class fields generated by coordinates of elliptic curves
• A proof of Sugawara's conjecture on Hasse-Weber ray class invariants
• An Application of the Dedekind-Hasse Criterion
• Ray class invariants over imaginary quadratic fields