The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields
Let Hλ4 be the Hecke group x,y:x2=y4=1 and, for a square-free positive integer n, consider the subset ℚ∗−n=a+−n/c|a,b=a2+n/c∈ℤ, c∈2ℤ of the quadratic imaginary number field ℚ−n. Following a line of research in the relevant literature, we study the properties of the action of Hλ4 on ℚ∗−n. In particul...
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9323424 |
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| author | Abdulaziz Deajim |
| author_facet | Abdulaziz Deajim |
| author_sort | Abdulaziz Deajim |
| collection | DOAJ |
| description | Let Hλ4 be the Hecke group x,y:x2=y4=1 and, for a square-free positive integer n, consider the subset ℚ∗−n=a+−n/c|a,b=a2+n/c∈ℤ, c∈2ℤ of the quadratic imaginary number field ℚ−n. Following a line of research in the relevant literature, we study the properties of the action of Hλ4 on ℚ∗−n. In particular, we calculate the number of orbits arising from this action for every such n. Some illustrative examples are also given. |
| format | Article |
| id | doaj-art-bb22601803c14abea07ebd3ffdf90d27 |
| institution | DOAJ |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bb22601803c14abea07ebd3ffdf90d272025-08-20T03:23:27ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/93234249323424The Hecke Group Hλ4 Acting on Imaginary Quadratic Number FieldsAbdulaziz Deajim0Department of Mathematics, King Khalid University, P. O. Box 9004, Abha, Saudi ArabiaLet Hλ4 be the Hecke group x,y:x2=y4=1 and, for a square-free positive integer n, consider the subset ℚ∗−n=a+−n/c|a,b=a2+n/c∈ℤ, c∈2ℤ of the quadratic imaginary number field ℚ−n. Following a line of research in the relevant literature, we study the properties of the action of Hλ4 on ℚ∗−n. In particular, we calculate the number of orbits arising from this action for every such n. Some illustrative examples are also given.http://dx.doi.org/10.1155/2021/9323424 |
| spellingShingle | Abdulaziz Deajim The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields Journal of Mathematics |
| title | The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields |
| title_full | The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields |
| title_fullStr | The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields |
| title_full_unstemmed | The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields |
| title_short | The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields |
| title_sort | hecke group hλ4 acting on imaginary quadratic number fields |
| url | http://dx.doi.org/10.1155/2021/9323424 |
| work_keys_str_mv | AT abdulazizdeajim theheckegrouphl4actingonimaginaryquadraticnumberfields AT abdulazizdeajim heckegrouphl4actingonimaginaryquadraticnumberfields |