30 citations · 88 across the 16 of their papers we have counts for
18 papers
Counting rational points on weighted projective spaces over number fields
Peter Bruin, Irati Manterola Ayala
Deng (arXiv:math/9812082) gave an asymptotic formula for the number of rational points on a weighted projective space over a number field with respect to a certain height function.…
Extensions and torsors for finite group schemes
Peter Bruin
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with cent…
Elliptic curves with a point of order 13 defined over cyclic cubic fields
Peter Bruin, Maarten Derickx, Michael Stoll
We show that there is essentially a unique elliptic curve defined over a cubic Galois extension of with a -rational point of order 13 and such that is no…
Counting elliptic curves with prescribed level structures over number fields
Peter Bruin, Filip Najman
Harron and Snowden counted the number of elliptic curves over up to height with torsion group for each possible torsion group over . In this pa…
On quantum computation of Kloosterman sums
Peter Bruin
We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field of elements. The first algorithm computes a quantum state contai…
Reductions of points on algebraic groups, II
Peter Bruin, Antonella Perucca
Let be the product of an abelian variety and a torus over a number field , and let be a positive integer. If is a point of infinite order, we consider the se…