Date of Completion
Field of Study
Doctor of Philosophy
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.
Lamoureux, Matthew, "Stirling's Formula in Number Fields" (2014). Doctoral Dissertations. 412.