Thesis advisor: Dubi Kelmer / In complex analysis, analytic continuation is a common and important tool to study the properties of complex functions. In this paper, we will introduce and define the global zeta function with an associated function f, where f is a polynomial with n variables with integer coefficients. With the usage of p-adic integration, we can conclude that the global zeta function is analytically continued to all s ∈ C when f is the sum of squares with n variables. / Thesis (BS) — Boston College, 2022. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Departmental Honors. / Discipline: Mathematics.