My Research

My Research

Research Interests

Analytic and combinatorial number theory

Elliptic curves and modular forms

Recent Publications/preprints

An upper bound for $B_2[g]$ sets to appear in J. of Number Theory.

Sieving by large integers and covering systems of congruences to appear in J. of AMS.

(joint with M. Filaseta, K. Ford, S. Konyagin and C. Pomerance)

Average Frobenius distribution of elliptic curves to appear in Acta Arith.

(joint with Kevin James)

Average size of $2$-Selmer groups of elliptic curves, I

(Trans. of AMS 358 (2006), no. 4, 1563--1584 )

On the quadratic twists of a family of elliptic curves

(to appear in Mathematika)

Average size of $2$-Selmer groups of elliptic curves, II

(Acta Arith. 117 (2005), no. 1, 1--33)

$E$-symmetric numbers

(Colloq. Math., 103 (2005), no. 1, 17--25)

The qudratic Waring-Goldbach problem

(joint with J.Y. Liu and T. Wooley, J. Number Theory, 107 (2004), no. 2, 298--321)

Rank $0$ quadratic twists of a family of elliptic curves

(Compositio. Math., 135 (2003), no. 3, 331--356)

A note on the divisibility of class numbers of real quadratic fields

(J. Number Theory, 97 (2002), no. 1, 35--44)