V. Arul

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20182021

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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.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.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…

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

On the ℓ-adic valuation of certain Jacobi sums

Computing Zeta Functions of Cyclic Covers in Large Characteristic

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