Richard Griffon

activity

20162025

most citedOn the arithmetic of a family of twisted constant elliptic curves

5 citations · 19 across the 9 of their papers we have counts for

collaborators

11 papers

math.NT2025

A parallelogram height inequality for Drinfeld modules

Liam Baker, Richard Griffon, Fabien Pazuki

We prove an inequality relating the Taguchi heights of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the analogue for Drinfeld modules of t…

math.NT2025

Variation of height in an isogeny class over a function field

Richard Griffon, Samuel Le Fourn, Fabien Pazuki

We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any c…

math.NT2021

On the arithmetic of a family of superelliptic curves

Sarah Arpin, Richard Griffon, Libby Taylor +1

Let $p$ be a prime, let $r$ and $q$ be powers of $p$ , and let $a$ and $b$ be relatively prime integers not divisible by $p$ . Let $C / F_{r} (t)$ be the superelliptic curve wit…

math.NT2020

Isogenies of elliptic curves over function fields

Richard Griffon, Fabien Pazuki

We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the $j$ -invariant in an isogeny class. Th…

math.NT2019★ 1 cited

Elliptic curves with large Tate-Shafarevich groups over $F_{q} (t)$

Richard Griffon, Guus de Wit

Let $F_{q}$ be a finite field of odd characteristic $p$ . We exhibit elliptic curves over the rational function field $K = F_{q} (t)$ whose Tate-Shafarevich groups are…

math.NT2019★ 5 cited

On the arithmetic of a family of twisted constant elliptic curves

Richard Griffon, Douglas Ulmer

Let $F_{r}$ be a finite field of characteristic $p > 3$ . For any power $q$ of $p$ , consider the elliptic curve $E = E_{q, r}$ defined by $y^{2} = x^{3} + t^{q} - t$ over $K=\mathbb{F}_r(t…

math.NT2018

A new family of elliptic curves with unbounded rank

Richard Griffon

Let $F_{q}$ be a finite field of odd characteristic and $K = F_{q} (t)$ . For any integer $d \geq 2$ coprime to $q$ , consider the elliptic curve $E_{d}$ over $K$ defined by…

math.NT2018★ 3 cited

Bounds on special values of L-functions of elliptic curves in an Artin-Schreier family

Richard Griffon

In this paper, we study a certain Artin--Schreier family of elliptic curves over the function field $F_{q} (t)$ . We prove an asymptotic estimate on the size of the special va…

math.NT2017★ 1 cited

Explicit L-functions and a Brauer-Siegel theorem for Hessian elliptic curves

Richard Griffon

For a finite field $F_{q}$ of characteristic $p \geq 5$ and $K = F_{q} (t)$ , we consider the family of elliptic curves $E_{d}$ over $K$ given by $y^{2} + x y - t^{d} y = x^{3}$ for all…

math.NT2017★ 4 cited

Analogue of the Brauer-Siegel theorem for Legendre elliptic curves

Richard Griffon

We prove an analogue of the Brauer-Siegel theorem for the Legendre elliptic curves over $F_{q} (t)$ . More precisely, if $d$ is an integer coprime to $q$ , we denote by $E_{d}$ t…

math.NT2016★ 5 cited

A Brauer-Siegel theorem for Fermat surfaces over finite fields

Richard Griffon

We prove an analogue of the Brauer-Siegel theorem for Fermat surfaces over a finite field. Namely, letting $F_{d}$ be the Fermat surface of degree $d$ over $F_{q}$ and $p_g(F_…

A parallelogram height inequality for Drinfeld modules

Variation of height in an isogeny class over a function field

On the arithmetic of a family of superelliptic curves

Isogenies of elliptic curves over function fields

Elliptic curves with large Tate-Shafarevich groups over Fq​(t)

On the arithmetic of a family of twisted constant elliptic curves

A new family of elliptic curves with unbounded rank

Bounds on special values of L-functions of elliptic curves in an Artin-Schreier family

Explicit L-functions and a Brauer-Siegel theorem for Hessian elliptic curves

Analogue of the Brauer-Siegel theorem for Legendre elliptic curves

A Brauer-Siegel theorem for Fermat surfaces over finite fields

Elliptic curves with large Tate-Shafarevich groups over $F_{q} (t)$