V. Arul

collaborators

4 papers

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

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…

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

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