V. Arul

activity

20182022

most citedComputing Zeta Functions of Cyclic Covers in Large Characteristic

1 citations · 1 across the 6 of their papers we have counts for

collaborators

7 papers

math.NT2022

Rational points on $X_{0}^{+} (125)$

Vishal Arul, J. Steffen Müller

We compute the rational points on the Atkin-Lehner quotient $X_{0}^{+} (125)$ using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the cur…

math.NT2021

Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6

Nikola Adžaga, Vishal Arul, Lea Beneish +4

We use the method of quadratic Chabauty on the quotients $X_{0}^{+} (N)$ of modular curves $X_{0} (N)$ by their Fricke involutions to provably compute all the rational points of these curv…

math.NT2021

Doubly isogenous genus-2 curves with $D_{4}$ -action

Vishal Arul, Jeremy Booher, Steven R. Groen +5

We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over…

math.AG2019

Torsion points on Fermat quotients of the form $y^{n} = x^{d} + 1$

Vishal Arul

We classify all geometric torsion points on the Fermat quotients $y^{n} = x^{d} + 1$ where $n, d \geq 2$ are coprime. In addition, we classify all geometric torsion points on the generi…

math.NT2019

On the $ℓ$ -adic valuation of certain Jacobi sums

Vishal Arul

Fix distinct primes $ℓ$ and $f$ , a finite field $F_{q}$ such that $q \equiv 1 (mod ℓ f)$ , and a character $χ : F_{q}^{\times} \to C^{\times}$ of ex…

math.AG2018

Division by $1 - ζ$ on superelliptic curves and jacobians

Vishal Arul

In 2016, Yuri Zarhin gave formulas for "dividing a point on a hyperelliptic curve by 2." Given a point $P$ on a hyperelliptic curve $C$ , Zarhin gives the Mumford's repres…

math.NT2018★ 1 cited

Computing Zeta Functions of Cyclic Covers in Large Characteristic

Vishal Arul, Alex J. Best, Edgar Costa +2

We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic $p$ that runs in time $p^{1/2 + o (1)}$ . We conf…

Rational points on X0+​(125)

Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6

Doubly isogenous genus-2 curves with D4​-action

Torsion points on Fermat quotients of the form yn=xd+1

On the ℓ-adic valuation of certain Jacobi sums

Division by 1−ζ on superelliptic curves and jacobians

Computing Zeta Functions of Cyclic Covers in Large Characteristic

Rational points on $X_{0}^{+} (125)$

Doubly isogenous genus-2 curves with $D_{4}$ -action

Torsion points on Fermat quotients of the form $y^{n} = x^{d} + 1$

On the $ℓ$ -adic valuation of certain Jacobi sums

Division by $1 - ζ$ on superelliptic curves and jacobians