Reciprocity in the Hecke Groups

2023/07/02 by Debattam Das, Das, Debattam, Krishnendu Gongopadhyay +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2307.00496

Abstract

An element g in a group G is called reciprocal if there exists h ∈ G such that g^-1=hgh^-1. The reciprocal elements are also known as `real elements' or `reversible elements' in the literature. We classify the reciprocal elements and parametrize the reciprocal classes in the Hecke groups Γ_p for p≥ 3. This generalizes a result by Sarnak for reciprocal elements in the modular group.

Cited by

• Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups
• Counting Reciprocal Hyperbolic Elements in Hecke Groups
• Counting and equidistribution of strongly reversible closed geodesics in negative curvature

Related

• Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups
• K-groups of reciprocity functors
• Spherical growth of reciprocal classes in the Hecke Groups
• Reciprocity law for compatible systems of abelian mod p Galois representations
• Quadratic reciprocity in a finite group