Sayı cisimleri üzerindeki asal ideal teoremi

In this study, our aim is to present a proof of the prime ideal theorem. It states that there is an asymptotic formula for the function defined as the number of prime ideals with norm at most n in the ring of integers of a number field. In fact, it is a number field generalization of the prime number theorem. The prime ideal theorem was proved by Edmund Landau in 1903. In Landau's original proof, he gave an asymptotic formula with an error term for the number of prime ideals whose norms are less than or equal to n. In this thesis, using a weak version of the Wiener Ikehara Tauberian Theorem we will give another proof for the prime ideal theorem without an error term.