## Publications and Research

#### Title

An In-depth Look at p-adic Numbers

Poster

5-11-2020

#### Abstract

In this study, we consider $p$-adic numbers. We will also study the $p$-adic norm representation of real number, which is defined as $\mathbb{Q}_p = \{\sum_{j=m}^{\infty }a_j p^j: a_j \in \mathbb{D}_p, m\in\mathbb{Z}, a_m\neq 0\} \cup \{0\}$, where $p$ is a prime number. We explore properties of the $p$-adics by using examples. In particular, we will show that $\sqrt{6},i \in \mathbb{Q}_5$ and $\sqrt{2} \in \mathbb{Q}_7$. $p$-adic numbers have a wide range of applicationsnin fields such as string theory, quantum mechanics, and transportation in porous disordered media in geology.

#### Comments

This poster was presented at the 32nd Semi-Annual Honors and Undergraduate Research Scholars Poster Presentation at New York City College of Technology, May 11, 2020. Mentor: Professor Satyanand Singh (Mathematics).

COinS