5 citations · 5 across the 2 of their papers we have counts for
6 papers
On the arithmetic of a family of superelliptic curves
Sarah Arpin, Richard Griffon, Libby Taylor +1
Let be a prime, let and be powers of , and let and be relatively prime integers not divisible by . Let be the superelliptic curve wit…
The unit equation has no solutions in number fields of degree prime to where splits completely
Nicholas Triantafillou
Let be a number field with ring of integers . We prove that if does not divide and splits completely in , then the unit equation has…
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usual…
Dual linear programming bounds for sphere packing via modular forms
Henry Cohn, Nicholas Triantafillou
We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In…
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 that runs in time . We conf…
Efficient Point-Counting Algorithms for Superelliptic Curves
Matthew Hase-Liu, Nicholas Triantafillou
In this paper, we present efficient algorithms for computing the number of points and the order of the Jacobian group of a superelliptic curve over finite fields of prime order p.…