On a problem of Hasse and Ramachandra

On a problem of Hasse and Ramachandra

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

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2019-03, Vol.17 (1), p.131-140
Hauptverfasser: Koo, Ja Kyung, Shin, Dong Hwa, Yoon, Dong Sung
Format: Artikel
Sprache:eng
Schlagworte:
11G16
class field theory
complex multiplication
Fields (mathematics)
Number theory
Primary 11R37
Secondary 11G15
Weber function
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Beschreibung
Zusammenfassung:Let be an imaginary quadratic field, and let f be a nontrivial integral ideal of . Hasse and Ramachandra asked whether the ray class field of modulo f can be generated by a single value of the Weber function. We completely resolve this question when f = ( ) for any positive integer excluding 2, 3, 4 and 6.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0013