31 citations · 208 across the 28 of their papers we have counts for
5 papers · 1 filter
Elliptic curves over a finite field and the trace formula
Nathan Kaplan, Ian Petrow
We prove formulas for power moments for point counts of elliptic curves over a finite field such that the groups of -points of the curves contain a chosen subgroup. These fo…
Numerical Sets, Core Partitions, and Integer Points in Polytopes
Hannah Constantin, Benjamin Houston-Edwards, Nathan Kaplan
We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope.…
Traces of Hecke Operators and Refined Weight Enumerators of Reed-Solomon Codes
Nathan Kaplan, Ian Petrow
We study the quadratic residue weight enumerators of the dual projective Reed-Solomon codes of dimensions and over the finite field . Our main results are f…
The distribution of -points on cyclic -covers of genus
Alina Bucur, Chantal David, Brooke Feigon +4
We study fluctuations in the number of points of -cyclic covers of the projective line over the finite field when is fixed and the genus…
The Realization Problem for Delta Sets of Numerical Semigroups
Stefan Colton, Nathan Kaplan
The delta set of a numerical semigroup , denoted , is a factorization invariant that measures the complexity of the sets of lengths of elements in . We study the follow…