On Newton Polygons

Senior Capstone Experience by Brenda Clark ’21

Submitted to the Department of Mathematics

Advised by Dr. Emerald Stacy

Description: In school, we are taught that there is an absolute value function, but in fact, there are an infinite number of absolute value functions. If we complete the rational numbers under the traditional absolute value function, we obtain the real line. If instead, we complete the rational numbers under a p-adic absolute value, we obtain “the field of p-adic numbers.” This paper will explore the field of p-adic numbers, and how to use Newton Polygons to determine splitting behavior of polynomials over Qp.

Read Brenda’s SCE below:

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