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.

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