Kiseok Yeon

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20192026

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10 papers · 1 filter

math.NT2026

On two forms in many variables of different degrees

Kiseok Yeon

In this paper, we investigate integral solutions satisfying the system of two forms in many variables of different degrees. Let $d_{1}$ and $d_{2}$ be natural numbers with $d_2>d_1\geq…

math.NT2026

On weighted forms in many variables

Daniel Flores Galiote, Kiseok Yeon

In this paper, we introduce several novel approaches utilizing the circle method to obtain the asymptotic formula for the number of integral points of bounded height lying on a hyp…

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.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…

math.NT2025

The Hasse principle for random homogeneous polynomials in thin sets

Daniel Flores, Kiseok Yeon

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

math.NT2023

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 $⟨ a, ν_{d, n} (x)⟩ \in Z [x]$ be a homogeneous polynomial i…

math.NT2023

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.NT2022

Small fractional parts of polynomials and mean values of exponential sums

Kiseok Yeon

Let $k_{i} (i = 1, 2, \dots, t)$ be natural numbers with $k_{1} > k_{2} > \dots > k_{t} > 0$ , $k_{1} \geq 2$ and $t < k_{1} .$ Given real numbers $α_{j i} (1 \leq j \leq t, 1 \leq i \leq s)$ , we consider polyn…

math.NT2022

Small fractional parts of binary forms

Kiseok Yeon

We obtain bounds on fractional parts of binary forms of the shape $Ψ (x, y) = α_{k} x^{k} + α_{l} x^{l} y^{k - l} + α_{l - 1} x^{l - 1} y^{k - l + 1} + \dots + α_{0} y^{k}$ with $α_{k}, α_{l}, \dots, α_{0} \in R$ an…