The Hecke Group Hλ4 Acting on Imaginary Quadratic Number Fields

Abdulaziz Deajim and Shaofang Hong

Journal of Mathematics, 2021, vol. 2021, 1-11

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9323424

DOI: 10.1155/2021/9323424

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