The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes
Number Theory
2023-09-29 v1
Abstract
We examine the behavior of the sequences of -adic valuations of quadratic polynomials with integer coefficients for an odd prime through tree representations. Under this representation, a finite tree corresponds to a periodic sequence, and an infinite tree corresponds to an unbounded sequence. We use the polynomial coefficients to determine whether the -adic valuation trees are finite or infinite, the number of infinite branches, the number of levels, the valuations at terminating nodes, and their relationship to the corresponding sequences.
Cite
@article{arxiv.2309.16637,
title = {The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes},
author = {Will Boultinghouse and Emily Hammett and Stephen Hu and Olena Kozhushkina and Rachel Snyder and Justin Trulen},
journal= {arXiv preprint arXiv:2309.16637},
year = {2023}
}