D. Zywina

activity

20082026

most citedElliptic curves with maximal Galois action on their torsion points

37 citations · 235 across the 35 of their papers we have counts for

collaborators

37 papers

math.NT2026

On the infinitude of elliptic curves over a number field with prescribed small rank

David Zywina

For any number field $K$ and integer $0 \leq r \leq 4$ , we prove that there are infinitely many elliptic curves over $K$ of rank $r$ . Our elliptic curves are obtained by specializin…

math.NT2025

Rank one elliptic curves and rank stability

David Zywina

For any quadratic extension $L / K$ of number fields, we prove that there are infinitely many elliptic curves $E$ over $K$ so that the abelian groups $E (K)$ and $E (L)$ both have rank…

math.NT2025

There are infinitely many elliptic curves over the rationals of rank 2

David Zywina

We show that there are infinitely many elliptic curves $E / Q$ , up to isomorphism over $Q$ , for which the finitely generated group $E (Q)$ has ra…

math.NT2025

Drinfeld modules with maximal Galois action

David Zywina

With a fixed prime power $q > 1$ , define the ring of polynomials $A = F_{q} [t]$ and its fraction field $F = F_{q} (t)$ . For each pair $a = (a_{1}, a_{2}) \in A^{2}$ with $a_{2}$ nonzer…

math.NT2025

An elliptic surface with infinitely many fibers for which the rank does not jump

David Zywina

Let $E$ be a nonisotrivial elliptic curve over $Q (T)$ and denote the rank of the abelian group $E (Q (T))$ by $r$ . For all but finitely many $t \in Q$ , spec…

math.NT2024

Improved bounds for integral points on modular curves using Runge's method

David Zywina

Consider a modular curve $X_{G}$ defined over a number field $K$ , where $G$ is a subgroup of $G L_{2} (Z / N Z)$ with $N > 2$ . The curve $X_{G}$ comes with a morphism $j: X_G\…