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Seon Jeong Kim

Publications and source records attributed to Seon Jeong Kim.

12 recordsLinked to original sources
arXiv2026

Rational points and inflexions on Hermitian-relative curves

In [6], we introduced the notion of a Hermitian-relative curve, which is a plane curve defined by $(x^{\sqrt{q}}, y^{\sqrt{q}}, z^{\sqrt{q}})A (x,y,z)^t =0$ with $A \in GL(3, \mathbb{F}_q)$. After investigating their basic properties, we classified those curves with two or more rational inflexions. In this paper, we first complete the classification of curves whose rational points are all inflexions by demonstrating the existence of curves with exactly one rational point. As a continuation, we then classify Hermitian-relative curves that possess at least one rational point which is not an inflexion. We categorize these curves according to the ordered pair consisting of the number of rational points and the number of inflexions. Finally, we enumerate all possible pairs and prove that each pair is realized by a suitable curve.

math.AG↗
arXiv2024

Relatives of the Hermitian curve

We introduce the notion of a relative of the Hermitian curve of degree $\sqrt{q}+1$ over $\mathbb{F}_q$, which is a plane curve defined by \[(x^{\sqrt{q}}, y^{\sqrt{q}}, z^{\sqrt{q}})A {}^t \!(x,y,z) =0\] with $A \in GL(3, \mathbb{F}_q)$, and study their basic properties, one of which is that the number of $\mathbb{F}_q$-points of any relative of the Hermitian curve of degree $\sqrt{q}+1$ is congruent to $1$ modulo $\sqrt{q}$. In the latter part of this paper, we classify those curves having two or more rational inflexions.

math.AG↗
arXiv2020

Frequency-tunable nano-oscillator based on Ovonic Threshold Switch (OTS)

Nano-oscillator devices are gaining more and more attention as a prerequisite for developing novel energy-efficient computing systems based on coupled oscillators. Here, we introduce a highly scalable, frequency-tunable nano-oscillator consisting of one Ovonic threshold switch (OTS) and a field-effect transistor (FET). It is presented that the proposed device shows an oscillating behavior with a natural frequency (f_{nat}) adjustable from 0.5 to 2 MHz depending on the gate voltage applied to the FET. In addition, under a small periodic input, it is observed that the oscillating frequency (f_{osc}) of the device is locked to the frequency (f_{in}) of the input when f_{in} ~ f_{nat}, demonstrating the so-called synchronization phenomenon. It also shows the phase lock of the combined oscillator network using circuit simulation, where the phase relation between the oscillators can be controlled by the coupling strength. These results imply that the proposed device is promising for applications in oscillator-based computing systems.

cond-mat.mtrl-sci↗
arXiv2016

Number of points of a nonsingular hypersurface in an odd-dimensional projective space

The numbers of $\mathbb{F}_q$-points of nonsingular hypersurfaces of a fixed degree in an odd-dimensional projective space are investigated, and an upper bound for them is given. Also we give the complete list of nonsingular hypersurfaces each of which realizes the upper bound. This is a natural generalization of our previous study of surfaces in projective $3$-space.

math.AG↗
arXiv2014

Numbers of points of surfaces in the projective $3$-space over finite fields

In the previous paper, we established an elementary bound for numbers of points of surfaces in the projective $3$-space over ${\Bbb F}_q$. In this paper, we give the complete list of surfaces that attain the elementary bound. Precisely those surfaces are the hyperbolic surface, the nonsingular Hermitian surface, and the surface of minimum degree containing all ${\Bbb F}_q$-points of the $3$-space.

math.AG↗
arXiv2011

Rational curves with many rational points over a finite field

We study a particular plane curve over a finite field whose normalization is of genus 0. The number of rational points of this curve achieves the Aubry-Perret bound for rational curves. The configuration of its rational points and a generalization of the curve are also presented.

math.AG↗
arXiv2009

Nonsingular plane filling curves of minimum degree over a finite field and their automorphism groups: Supplements to a work of Tallini

Our concern is a nonsingular plane curve defined over a finite field of q elements which includes all the rational points of the projective plane over the field. The possible degree of such a curve is at least q+2. We prove that nonsingular plane curves of degree q+2 having the property actually exist. More precisely, we write down explicitly all of those curves. Actually, Giuseppe Tallini studied such curves in his old paper in 1961. We explain the connection between his work and ours. Moreover we give another proof of his result on the automorphism group of such a curve, from the viewpoint of linear algebra.

math.AG↗