Sungsoo Na

Attracting fixed points of Dedekind zeta functions

Every Dedekind zeta function has a unique fixed point on (1, infinity), but this point need not be repelling. We give certified attracting examples in a real quadratic field and four abelian fields, each with a certified repelling real two-cycle. Two arithmetic limits explain the...

The number of regions determined by all (d-1)-simplices spanned by a point set in R^d

Let S be a set of n points in strong general position in R^d, d ≥ 2, and let Σ_d be the union of the C(n,d) closed (d−1)-simplices spanned by S. We study R_d(S), the number of connected components of int conv S \ Σ_d, extending the exact theory available for d = 3. The cells of t...

A Schwarzian inequality for the Riemann zeta function and its real dynamics

We prove a two-sided moment inequality for the Riemann zeta function: for $A_j(s)=\sum_{n\ge2}(\log n)^j n^{-s}$, one has $A_2(s)^2< A_1(s)A_3(s)<\tfrac32 A_2(s)^2$ for every $s>1$. The upper bound is equivalent to negativity of the Schwarzian derivative, whose endpoint limits ar...

A Schwarzian inequality for the Riemann zeta function and its real dynamics

We prove a two-sided moment inequality for the Riemann zeta function: for $A_j(s)=\sum_{n\ge2}(\log n)^j n^{-s}$, one has $A_2(s)^2< A_1(s)A_3(s)<\tfrac32 A_2(s)^2$ for every $s>1$. The upper bound is equivalent to negativity of the Schwarzian derivative, whose endpoint limits ar...

The number of regions determined by all (d-1)-simplices spanned by a point set in R^d

Let S be a set of n points in strong general position in R^d, d ≥ 2, and let Σ_d be the union of the C(n,d) closed (d−1)-simplices spanned by S. We study R_d(S), the number of connected components of int conv S \ Σ_d, extending the exact theory available for d = 3. The cells of t...

Two Algebraic Thresholds for Relaxations of Stable Metric TSP

Bilu–Linial stability asks whether an optimal solution remains uniquely optimal after every independent multiplicative increase of the input costs by a prescribed factor. For symmetric metric TSP, every 1.8-stable instance is solvable in polynomial time, and both the subtour rela...

Two Algebraic Thresholds for Relaxations of Stable Metric TSP

Bilu–Linial stability asks whether an optimal solution remains uniquely optimal after every independent multiplicative increase of the input costs by a prescribed factor. For symmetric metric TSP, every 1.8-stable instance is solvable in polynomial time, and both the subtour rela...