Graduation Year
2025
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
Reader 2
Yifeng Huang
Reader 3
Ken Ono
Terms of Use & License Information
Rights Information
2025 Daniel Vargas
Abstract
Motivated by classical works of Gauss and Euler on the AGM, Ono and his
collaborators Griffin et al. (2023); McSpirit and Ono (2023) have investigated
the union of AGM sequences over finite fields π½π, where π β‘3 mod 4. A
recent preprint Kayath et al. (2024) extends some of their results to all finite
fields with odd characteristic. We refine these works when πβ‘5 mod 8. In
particular, we explicitly determine the components of these graphs and their
total population. We also use Galois-theoretic results to make progress in
the search for cycles over finite fields with odd characteristic.
Recommended Citation
Vargas, Daniel, "GaloisTheory and the Arithmetic-Geometric Series" (2025). HMC Senior Theses. 288.
https://scholarship.claremont.edu/hmc_theses/288
