Goresky and Klapper conjectured that for any prime p > 13 and any `-sequence a based on p, every pair of allowable decimations of a is cyclically distinct. The conjecture is essentially equivalent toâ€¦ (More)

Given a fixed genus g, we would like to know the largest possible integer t such that t copies of one elliptic curve E appear in the decomposition of the Jacobian variety JX for some curve X of genusâ€¦ (More)

We decompose the Jacobian variety of hyperelliptic curves up to genus 10, defined over an algebraically closed field of characteristic zero, with reduced automorphism group A4, S4, or A5. Among thoseâ€¦ (More)

For any prime `, it is possible to construct global function fields whose Jacobians have high `-rank by moving to a sufficiently large constant field extension. This was investigated in some detailâ€¦ (More)

Let p be an odd prime, k, A âˆˆ Z, p A, d = (p âˆ’ 1, k), d1 = (p âˆ’ 1, k âˆ’ 1), s = (p âˆ’ 1)/d, t = (p âˆ’ 1)/d1, E the set of even residues in Zp = Z/(p), O the set of odd residues, and Nk = #{x âˆˆ E : Axk âˆˆâ€¦ (More)

Many interesting questions can be asked about the decomposition of Jacobians of curves. For instance, we may want to know which curves have completely decomposable Jacobians (Jacobians which are theâ€¦ (More)

My primary research interests lie in two distinct branches of number theory. I explore decompositions of Jacobian varieties of curves and related arithmetic geometry problems. I also study questionsâ€¦ (More)

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new methodâ€¦ (More)