Arithmetic-geometric mean sequences over finite fields $\mathbb{F}_q$, where $q\equiv5\pmod{8}$

TL;DR

This paper extends the study of arithmetic-geometric mean sequences to finite fields where q ≡ 5 mod 8, exploring their properties and connections with graph theory, building on prior work over other finite fields.

Contribution

It introduces a new definition of arithmetic-geometric mean sequences over finite fields with q ≡ 5 mod 8 and analyzes their graph-theoretic properties.

Findings

Sequences are well-defined over $inite fields$ with q ≡ 5 mod 8

Connections established between sequences and graph structures

Properties of the associated graphs are characterized

Abstract

Arithmetic-geometric mean sequences were already studied over real and complex numbers, and recently, Michael J. Griffin, Ken Ono, Neelam Saikia and Wei-Lun Tsai considered them over finite fields $\mathbb{F}_q$ such that $q \equiv 3 \pmod 4$. In this paper, we extend the definition of arithmetic-geometric mean sequences over $\mathbb{F}_q$ such that $q \equiv 5 \pmod 8$. We explain the connection of these sequences with graphs and show the properties of the corresponding graphs in the case $q \equiv 5 \pmod 8$.