A Brief Introduction to Splitting Of Primes over Number Fields

The study of Dedekind Zeta Functions over a number field extension uses different aspects of both Algebraic and Analytic Number Theory. In this paper, we shall learn about the structure and different analytic aspects of such functions, namely the domain of its convregence and analyticity at different points of ℂ when the function is defined over any finite field extension K over ℚ . Moreover, given any two Number Fields L and K over ℚ with L being Normal over K, our intention is to classify and study the primes in K which split completely in L. Also, we shall explore some special cases related to this result