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ARITHMETIC-GEOMETRIC MEAN SEQUENCES OVER FINITE FIELDS
$\mathbb {F}_q$, WHERE 
$q\equiv 5$ (mod 8)
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 27 February 2025, pp. 1-12
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- Article
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Arithmetic-geometric mean sequences were already studied over the real and complex numbers, and recently, Griffin et al. [‘AGM and jellyfish swarms of elliptic curves’, Amer. Math. Monthly 130(4) (2023), 355–369] considered them over finite fields
$\mathbb {F}_q$ for 
$q \equiv 3 \pmod 4$. We extend the definition of arithmetic-geometric mean sequences over 
$\mathbb {F}_q$ to 
$q \equiv 5 \pmod 8$. We explain the connection of these sequences with graphs and explore the properties of the graphs in the case where 
$q \equiv 5 \pmod 8$.
