Niven Achenjang

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20182024

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math.NT2023

The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2

Niven Achenjang

Let $K$ be the function field of a smooth curve $B$ over a finite field $k$ of arbitrary characteristic. We prove that the average size of the $2$ -Selmer groups of elliptic curves…

math.NT2022

Integral points on varieties with infinite étale fundamental group

Niven T. Achenjang, Jackson S. Morrow

We study integral points on varieties with infinite étale fundamental groups. More precisely, for a number field $F$ and $X / F$ a smooth projective variety, we prove that for any ge…

math.NT2018

On Gaps in the Closures of Images of Divisor Functions

Niven Achenjang, Aaron Berger

Given a complex number $c$ , define the divisor function $σ_{c} : N \to C$ by $σ_{c} (n) = \sum_{d ∣ n} d^{c}$ . In this paper, we look at $σ_{- r} (N)$ , the top…