arXiv subjects

Jeffrey Hatley

Publications and source records attributed to Jeffrey Hatley.

20 records · Page 2Linked to original sources

arXiv2014

Obstruction criteria for modular deformation problems

For a newform $f=\sum a_n q^n$ of weight $k \geq 3$ and a prime $λ$ of $\mathbf{Q}(a_n)$, the deformation problem for its associated mod $λ$ Galois representation is unobstructed for all primes outside some finite set. Previous results gave an explicit bound on this finite set for $f$ of squarefree level; we modify this bound and remove the squarefree hypothesis. We also show that if the $λ$-adic deformation problem for $f$ is unobstructed, then $f$ is not congruent mod $λ$ to a newform of lower level.

math.NT↗

arXiv2009

On the Rank of the Elliptic Curve y^2=x(x-p)(x-2)

An elliptic curve E defined over \Q is an algebraic variety which forms a finitely generated abelian group, and the structure theorem then implies that E = \Z^r + \Z_{tors} for some r \geq 0; this value r is called the rank of E. It is a classical problem in the study of elliptic curves to classify curves by their rank. In this paper, the author uses the method of 2-descent to calculate the rank of two families of elliptic curves, where E is given by E: y^2 = x(x-p)(x-2) with p, p-2 being twin primes.

math.NT↗