The study of \textit{ Dedekind Zeta Functions} over a number field extension uses different aspects of both \textit{ Algebraic} and \textit{ 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 $\mathbb{ C}$ when the function is defined over any finite field extension $K$ over $\mathbb{ Q}$ . Moreover, given any two Number Fields $L$ and $K$ over $\mathbb{ Q}$ 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.
Categories: math.HO