1. A local-global principle for images of Galois representations, submitted. pdf
  2. Evaluations of cubic twisted Kloosterman sheaf sums. Int. J. Number Theory, 6 no. 6 (2010), pp. 1349-1365. (Joint with J. Booher and A. Hittson) pdf
  3. Powers of the eta-function and Hecke operators. Int. J. Number Theory, 8 no. 3 (2012), pp. 599 - 611. (Joint with A. Carney and S. Pitman) pdf
  4. On the ranks of the Jacobians of curves defined by Jacobi polynomials. Rocky Mountain J. Math., 44 no. 1 (2014), pp. 23 - 33. (Joint with J. Cullinan and E. Sell) pdf

In Preparation

  1. A classification of algebraic function fields with class number 3.
  2. How often is the discriminant of a polynomial over a finite field a kth power? (Joint with R. Moy, J. Specter, and A. Tripathy)
  3. Sporadic Torsion on Elliptic Curves. (Joint with J. Morrow and D. Zureick-Brown)
  4. Explicit Brauer-Manin obstructions for 9-nodal cubic threefolds (Joint with M. Pieropan and B. Frankel)
  5. Rational points on diagonal del Pezzo surfaces of degree 2.


  1. "Class numbers of algebraic function fields, or Jacobians of curves over finite fields," AMS Special Session on Number Theory and Cryptography at the 2016 Joint Mathematics Meetings in Seattle, WA. pdf