Properties of the Dirichlet Series of a Family of Counting Functions

Abstract

In this thesis, we follow reasonably closely the arguments for proving [1, Prop 1.7] for an alternate case. In particular, the aforementioned result is focusing on counting functions of number fields where all elements of a finite set of arbitrary non-archimidean places split completely under arbitrary local conditions, whereas we will be focusing on counting functions where all elements in such a set instead ramify. The general methods of proving the original result largely work here, but many of the specific details end up changing for our case. We also make one of the implicit dependencies from the original result explicit for our result, as if we in future wish to use this for applications similar to those found in [1], this would be important.

Date of Award	4 Nov 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Marcus Tressl (Main Supervisor) & Martin Orr (Co Supervisor)