Kiseok Yeon

collaborators

6 papers

math.NT2026

On the density of rational lines on diagonal cubic hypersurfaces, II

Scott Parsell, Kiseok Yeon

In this paper, we establish the expected asymptotic formula for the number of rational lines on a diagonal cubic hypersurface in 18 or more variables, improving on recent work of t…

math.NT2026

On the density of rational lines on diagonal cubic hypersurfaces

Kiseok Yeon

In this paper, we establish the asymptotic estimates for the rational lines on diagonal cubic hypersurfaces defined by $\sum_{i = 1}^{s} c_{i} x_{i}^{3} = 0$ with $c_i\in\mathbb{Z}\setminus \{0\…

math.NT2026

The Hasse principle for random homogeneous polynomials in thin sets

Daniel Flores, Kiseok Yeon

Let $d$ and $n$ be natural numbers. Let $I^½_{d, n} : R^{n} \to R^{N}$ denote the Veronese embedding with $N = N_{n, d} := (d n + d - 1)$ , defined by listing all…

math.NT2025

The local solubility for homogeneous polynomials with random coefficients over thin sets

Heejong Lee, Seungsu Lee, Kiseok Yeon

Let $d$ and $n$ be natural numbers greater or equal to $2$ . Let $⟨ a, I^½_{d, n} (x)⟩ \in Z [x]$ be a homogeneous polynomial…

math.NT2025

The Hasse principle for homogeneous polynomials with random coefficients over thin sets

Kiseok Yeon

In this paper, we investigate the solubility of homogeneous polynomial equations. The work of Browning, Le boudec, Sawin [3] shows that almost all homogeneous equations of degree $…

math.NT2025

An extended Vinogradov's mean value theorem

Changkeun Oh, Kiseok Yeon

In this paper, we provide novel mean value estimates for exponential sums related to the extended main conjecture of Vinogradov's mean value theorem, by developing the Hardy-Little…