I’m a PhD student of Jeff Hoffstein at Brown University. I research topics related to analytic number theory. My interests include $L$-functions, automorphic forms, metaplectic forms, Multiple Dirichlet Series, arithmetic geometry, and related topics.

On the side, I also enjoy looking into topics related to the mean value theorem of calculus. (Yes, really. It’s for fun, but it turns out that a lot of nice depth lurks behind some simple questions).

### Current and Recent Papers

- On Some Variants of the Gauss Circle Problem, PhD Thesis, arXiv preprint, github repository. Chapters 3 and 4 includes much material published elsewhere. Chapters 5 and 6 first appear in the thesis.
- The Laplace Transform of the Second Moment in the Gauss Circle Problem, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint,
*submitted.* - Second Moments in the Generalized Gauss Circle Problem, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint,
*submitted.* - Traces, high powers and one level density for families of curves over finite fields, with Alina Bucur, Edgar Costa, Chantal David, and João Guerreiro, arXiv preprint,
*To appear in*.**Mathematical Proceedings of the Cambridge Philsophical Society** - On Functions whose Mean-Value Abscissas are Midpoints, with Paul Carter, arXiv preprint, paper announcement,
**American Mathematical****Monthly,**124.6 (2017): 535-542*.* - Sign-Changes of Sums of Fourier Coefficients of Cusp Forms, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcement,
**Journal of Number Theory**, 177 (2017): 112-135*.* - Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcement,
**Journal of Number Theory**, 173 (2017): 394-415*.* -
The Second Moment of Sums of Coefficients of Cusp Forms, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcement,
**Journal of Number Theory**, 173 (2017): 304-331*.* - Taylor’s Theorem and a General Order Mean Value Theorem,
*Submitted.* - Unexpected Conjectures about -5 modulo primes,
*Classroom Capsule*,Vol 46 No 1, January 2015.*College Math Journal*,