Global, Local Zeta Function and p-adic Integration
Zhou, Zi Jie. “Global, Local Zeta Function and p-adic Integration”, Boston College, 2022. http://hdl.handle.net/2345/bc-ir:109434.
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.