On a problem of Hasse and Ramachandra
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-03-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0013 |
| _version_ | 1818738577623744512 |
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| author | Koo Ja Kyung Shin Dong Hwa Yoon Dong Sung |
| author_facet | Koo Ja Kyung Shin Dong Hwa Yoon Dong Sung |
| author_sort | Koo Ja Kyung |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T01:11:09Z |
| format | Article |
| id | doaj.art-3472bdbeef5e4a46ab65fa28c1909479 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-18T01:11:09Z |
| publishDate | 2019-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-3472bdbeef5e4a46ab65fa28c19094792022-12-21T21:26:06ZengDe GruyterOpen Mathematics2391-54552019-03-0117113114010.1515/math-2019-0013math-2019-0013On a problem of Hasse and RamachandraKoo Ja Kyung0Shin Dong Hwa1Yoon Dong Sung2Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of KoreaDepartment of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 17035, Republic of KoreaDepartment of Mathematics Education, Pusan National University, Busan, 46241, Republic of KoreaLet 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.https://doi.org/10.1515/math-2019-0013class field theorycomplex multiplicationweber functionprimary 11r37secondary 11g1511g16 |
| spellingShingle | Koo Ja Kyung Shin Dong Hwa Yoon Dong Sung On a problem of Hasse and Ramachandra Open Mathematics class field theory complex multiplication weber function primary 11r37 secondary 11g15 11g16 |
| title | On a problem of Hasse and Ramachandra |
| title_full | On a problem of Hasse and Ramachandra |
| title_fullStr | On a problem of Hasse and Ramachandra |
| title_full_unstemmed | On a problem of Hasse and Ramachandra |
| title_short | On a problem of Hasse and Ramachandra |
| title_sort | on a problem of hasse and ramachandra |
| topic | class field theory complex multiplication weber function primary 11r37 secondary 11g15 11g16 |
| url | https://doi.org/10.1515/math-2019-0013 |
| work_keys_str_mv | AT koojakyung onaproblemofhasseandramachandra AT shindonghwa onaproblemofhasseandramachandra AT yoondongsung onaproblemofhasseandramachandra |