Research

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

  1. 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.
  2. The Laplace Transform of the Second Moment in the Gauss Circle Problem, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprintsubmitted.
  3. Second Moments in the Generalized Gauss Circle Problem, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprintsubmitted.
  4. 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 preprintTo appear in Mathematical Proceedings of the Cambridge Philsophical Society.
  5. On Functions whose Mean-Value Abscissas are Midpoints, with Paul Carter, arXiv preprint, paper announcement American Mathematical Monthly, 124.6 (2017): 535-542.
  6. Sign-Changes of Sums of Fourier Coefficients of Cusp Forms, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcementJournal of Number Theory, 177 (2017): 112-135.
  7. 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.
  8. The Second Moment of Sums of Coefficients of Cusp Forms, with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcementJournal of Number Theory,  173 (2017): 304-331.
  9. Taylor’s Theorem and a General Order Mean Value Theorem, Submitted.
  10. Unexpected Conjectures about -5 modulo primes, Classroom Capsule,  College Math JournalVol 46 No 1, January 2015.

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