- Trace formulas and class number sums, Acta Arith. 132 (2008), no. 4,
- A bound for the torsion conductor of a non-CM elliptic curve, Proc.
Amer. Math. Soc. 137 (2009), 37-43.
- A refined version of the Lang-Trotter conjecture (joint with
Stephan Baier), Int. Math. Res. Not. IMRN 2009 (2009) no. 3, 433-461.
- Averages of elliptic curve constants, Math. Ann. 345 (2009) no. 3,
- Almost all elliptic curves are Serre curves, Trans. Amer. Math. Soc. 362
- Appendix to Geometry and arithmetic of verbal dynamical systems on simple
groups, by T. Bandman, F. Grunewald, B. Kunyavskii; in ``Groups, Geometry, and Dynamics'' (a volume
dedicated to W. Magnus) EMS Publishing House, 4 (2010) no. 4, 607-655.
- One-parameter families of elliptic curves over Q with maximal Galois
representations (joint with A.C. Cojocaru and D. Grant), Proc. Lond. Math. Soc. 103 (2011) no. 4,
- Pairs of elliptic curves with maximal Galois representations, J. Number Theory 133 (2013), 3381-3393.
- Elliptic aliquot cycles of fixed length, Pacific J. Math. 263 (2013) no. 2, 353-371.
- GL_2-representations with maximal image, Math. Res. Lett. 22 (2015) no. 3, 803-839.
- On primitivity of Dirichlet characters (joint with R. Daileda), International Journal of Number Theory 11 (2015), 1913-1939.
- Elliptic curves with 2-torsion contained in the 3-torsion field (joint with J. Brau), Proc. Amer. Math. Soc. 144 (2016), 925-936.
- A rigidity phenomenon for power maps, International Mathematics Research Notices 2017 (2017) no. 24, 7551--7579.
- Missing class groups and class number statistics for imaginary quadratic fields (joint with S. Holmin, P. Kurlberg, C. McLeman and K. Petersen), Experimental Mathematics 28 (2019) no. 2, 233--254.
- Constants in Titchmarsh divisor problems for elliptic curves (joint with R. Bell, C. Blakestad, A.C. Cojocaru, A. Cowan, V. Matei, G. Smith, and I. Vogt), Research in Number Theory 6 (2020) no. 1, Art. 1, 24 p.
- A bound for the conductor of an open subgroup of GL2 associated to an elliptic curve, to appear in Pacific J. Math.
- Degree bounds for the projective division fields associated to elliptic modules with a trivial endomorphism ring (joint with A.C. Cojocaru), preprint.
- The Lang-Trotter Conjecture for products of non-CM elliptic curves (joint with H. Chen and V. Serban), preprint.
- Elliptic curves with non-abelian entanglements (joint with K. McMurdy), preprint.
- The average asymptotic behaviour of the Frobenius fields of an elliptic curve (joint with A.C.
Cojocaru and H. Iwaniec), preprint (to be posted soon).
- Theta functions and modular correspondences, preprint (to be posted soon).