Date of Completion
5-8-2014
Embargo Period
5-8-2014
Major Advisor
Keith Conrad
Associate Advisor
Kyu-Hwan Lee
Associate Advisor
Alvaro Lozano-Robledo
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
In 1997 Bhargava generalized the factorial sequence to factorials in any Dedekind domain. He asked if there is an analogue of Stirling's formula for generalized factorials. Using techniques of analytic number theory, my thesis presents such an analogue when the Dedekind domain is the ring of integers in a number field. Unlike the classical case of Stirling's formula, which corresponds to the number field Q, its generalization to the factorials in a number field other than Q has a surprising ingredient: the formula involves a sum over nontrivial zeros of the zeta-function of the number field.
Recommended Citation
Lamoureux, Matthew, "Stirling's Formula in Number Fields" (2014). Doctoral Dissertations. 412.
https://digitalcommons.lib.uconn.edu/dissertations/412