Low-lying zeros in families of elliptic curve L-functions over function fields

We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists elliptic curves defined over Fq(T). In particular, we present precise expressions for expected values traces high powers Frobenius class these with a focus on lower order behavior. As an application obtain results one-level densities verify that curve have orthogonal symmetry type. twist our refine previous work Comeau-Lapointe. Moreover, this case find term density reminiscent deviation found by Rudnick hyperelliptic ensemble. On other hand, investigation is first treat questions it turns out be more complicated isolate terms due larger degree cancellation among contributions.