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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |