arXiv subjects

Young Deuk Kim

Publications and source records attributed to Young Deuk Kim.

8 recordsLinked to original sources

arXiv2025

Ordinality and Riemann Hypothesis II

For $\frac{1}{2} 0$, and $n\in\mathbb{N}$, let $\displaystyleθ_n(x+iy)=\sum_{i=1}^n\frac{\mbox{sgn}\, q_i}{q_i^{x+iy}}$, where $Q=\{q_1,q_2,q_3,\cdots\}$ is the set of finite products of distinct odd primes, and ${\mbox{sgn}}\, q=(-1)^k$ if $q$ is the product of $k$ distinct primes. In this paper, we prove that there exists an ordering of $Q$ such that the sequence $θ_n(x+iy)$ has a convergent subsequence. As an application, we study the Riemann hypothesis.

math.CV↗

arXiv2025

Ordinality and Riemann Hypothesis I

We present a sufficient condition for the Riemann hypothesis. This condition is the existence of a special ordering on the set of finite products of distinct odd primes.

math.NT↗

arXiv2025

On the Sum of Reciprocals of Primes

Suppose that $y>0$, $0\leqα<2π$, and $0 K$ and $P^-$ the set of primes $p$ such that $\cos(y\ln p+α)<-K$. In this paper, we prove $\sum_{p\in P^+}\frac{1}{p}=\infty$ and $\sum_{p\in P^-}\frac{1}{p}=\infty$.

math.GM↗

arXiv2007

Equivalent metrics and compactifications

Let (X,d) be a metric space and m\in X. Suppose that ϕ:X\times X\to\mathbold{R} is a nonnegative symmetric function. We define a metric d^{ϕ,m} on X which is equivalent to d. If d^{ϕ,m} is totally bounded, its completion is a compactification of (X,d). As examples, we construct two compactifications of (\mathhbold{R}^s,d_E), where d_E is the Euclidean metric and s\geq 2.

math.GT↗

arXiv2007

Locally Euclidean metrics on R^3

For all 0<t \leq 1, we define a locally Euclidean metric ρ_t on R^3. These metrics are invariant under Euclidean isometries and, if t increases to 1, converges to the Euclidean metric d_E. This research is motivated by expanding universe.

math.DG↗

arXiv2007

A family of pseudo metrics on B^3 and its application

Let B^3 be the closed unit ball in R^3 and S^2 its boundary. We define a family of pseudo metrics on B^3. As an application, We prove that for any countable-to-one function f:S^2\to [0,a], the set NM^n_f={x\in S^2 | there exists y\in S^2 such that f(x)-f(y)>nd_E(x,y)} is uncountable for all natural number n, where d_E is the Euclidean metric on R^3.

math.GN↗

arXiv2005

The Thurston boundary of Teichmuller space and complex of curves

Let $S$ be a closed orientable surface with genus $g\geq 2$. For a sequence $\s_i$ in the Teichmüller space of $S$, which converges to a projective measured lamination $[\lam]$ in the Thurston boundary, we obtain a relation between $\lam$ and the geometric limit of pants decompositions whose lengths are uniformly bounded by a Bers constant $L$. We also show that this bounded pants decomposition is related to the Gromov boundary of complex of curves.

math.GT↗

arXiv2003

A theorem on discrete, torsion free subgroups of Isom $H^n$

Let $H^n$ be the hyperbolic n-space with $n\geq 2$. Suppose that $Γ<Isom H^n$ is a discrete, torsion free subgroup and $a$ is a point in the domain of discontinuity $Ω(Γ)$. Let $p$ be the projection map from $H^n$ to the quotient manifold $M=H^n/Γ$. In this paper we prove that there exists an open neighborhood $U$ of $a$ in $H^n\cupΩ(Γ)$ such that $p$ is an isometry on $U\cap H^n$.

math.GT↗