14 citations · 34 across the 16 of their papers we have counts for
6 papers · 1 filter
Pointless Hyperelliptic Curves
Ryan Becker, Darren Glass
In this paper we consider the question of whether there exists a hyperelliptic curve of genus which is defined over $\FF_q$ but has no rational points over $\FF_q$ for various…
Compositions of Integers With Bounded Parts
Darren Glass
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as…
Curves of given -rank with trivial automorphism group
Jeff Achter, Darren Glass, Rachel Pries
Let be an algebraically closed field of characteristic . Suppose and . We prove there is a smooth projective -curve of genus and -ra…
The 2-ranks of Hyperelliptic Curves with Extra Automorphisms
Darren Glass
This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the…
Hyperelliptic Curves with Prescribed -Torsion
Darren Glass, Rachel Pries
In this paper, we show that there exist families of curves (defined over an algebraically closed field of characteristic ) whose Jacobians have interesting -torsion. F…
Invariants Associated to Orthogonal -constants
Darren Glass
In this paper we use the theory of -constants associated to tame finite group actions on arithmetic surfaces to define a Brauer group invariant $μ(\X,G,V)$ associated to certain…