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Research Interests
My primary research interests are in the broad fields of algebraic and analytic number theory. In particular, I am
interested in how zero-density estimates for families of L-functions can be used as substitutes for the Generalized
Riemann Hypothesis in the solution of certain number theoretic problems. In this regard I have spent a good deal
of time thinking about the extremal nature of class numbers of number fields. Through Trinity's REU I have also
dabbled somewhat in combinatorial number theory, considering certain divisibility properties of integers related to their
representations in various bases, as well as the asymptotic behavior of the repeated iteration of certain arithmetic
functions.
Research Articles
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An application of a generalization of Artin's primitive root conjecture in the theory of monoid rings, arXiv:2112.09080 [math.NT].
- Mutational meltdown in asexual populations doomed to
extinction, J. Math. Biol., 87:88 (2023).
- On primitivity of Dirichlet characters, Int. J. Number Theory, 11 (2015), no. 6, 1913--1939.
- Budding yeast, branching processes, and generalized Fibonacci
numbers, Math. Mag., 84 (2011), no. 3, 163--172.
- Maximal class numbers of CM number fields, J.
Number Theory 130 (2010), no. 4, 936--943.
- On the counting function for the generalized Niven
numbers, J. Théor.
Nombres Bordeaux 21 (2009), no. 3, 503--515.
- Non-abelian number fields with very large class
numbers, Acta Arith.
125 (2006), no. 3, 215--255.
- Algebraic integers on the unit circle, J.
Number
Theory 118 (2006), no. 2,
189--191.
- Extremal class numbers of non-abelian number fields, UCLA Ph.D. thesis (2004).
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