N. Kaplan

activity

20102024

most citedCounting Numerical Semigroups

31 citations · 208 across the 28 of their papers we have counts for

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12 papers · 1 filter

math.NT2023

The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I

John Cullinan, Nathan Kaplan

Let $ℓ$ be a prime number and let $E$ and $E^{'}$ be $ℓ$ -isogenous elliptic curves defined over a finite field $k$ of characteristic $p \neq = ℓ$ . Suppose the groups $E (k)$ and…

math.NT2022

Generalizations of results of Friedman and Washington on cokernels of random $p$ -adic matrices

Gilyoung Cheong, Nathan Kaplan

Let $p$ be prime and $X$ be a Haar-random $n \times n$ matrix over $Z_{p}$ , the ring of $p$ -adic integers. Let $P_{1} (t), \dots, P_{l} (t) \in Z_{p} [t]$ be monic p…

math.NT2020★ 5 cited

Counting Plane Cubic Curves over Finite Fields with a Prescribed Number of Rational Intersection Points

Nathan Kaplan, Vlad Matei

For each integer $k \in [0, 9]$ , we count the number of plane cubic curves defined over a finite field $F_{q}$ that do not share a common component and intersect in exactly $…

math.NT2018★ 4 cited

Weight enumerators of Reed-Muller codes from cubic curves and their duals

Nathan Kaplan

Let $F_{q}$ be a finite field of characteristic not equal to $2$ or $3$ . We compute the weight enumerators of some projective and affine Reed-Muller codes of order $3$ over…

math.NT2018★ 14 cited

Random Partitions and Cohen-Lenstra Heuristics

Jason Fulman, Nathan Kaplan

We investigate combinatorial properties of a family of probability distributions on finite abelian p-groups. This family includes several well-known distributions as specialization…

math.NT2017★ 2 cited

The cotype zeta function of $Z^{d}$

Gautam Chinta, Nathan Kaplan, Shaked Koplewitz

We give an asymptotic formula for the number of sublattices $Λ \subseteq Z^{d}$ of index at most $X$ for which $Z^{d} /Λ$ has rank at most $m$ , answering a question of…

math.NT2016★ 20 cited

Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks

Jennifer S. Balakrishnan, Wei Ho, Nathan Kaplan +3

Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes…

math.NT2015★ 14 cited

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 $k$ such that the groups of $k$ -points of the curves contain a chosen subgroup. These fo…

math.NT2015★ 4 cited

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 $5$ and $q - 4$ over the finite field $F_{q}$ . Our main results are f…

math.NT2015

The distribution of $F_{q}$ -points on cyclic $ℓ$ -covers of genus $g$

Alina Bucur, Chantal David, Brooke Feigon +4

We study fluctuations in the number of points of $ℓ$ -cyclic covers of the projective line over the finite field $F_{q}$ when $q \equiv 1 mod ℓ$ is fixed and the genus…

math.NT2014★ 1 cited

Distribution of orders in number fields

Nathan Kaplan, Jake Marcinek, Ramin Takloo-Bighash

In this paper we study the distribution of orders of bounded discriminants in number fields. We give an asymptotic formula for the number of orders contained in the ring of integer…

math.NT2010★ 1 cited

Counting Subrings of $Z^{n}$ of finite index