3 papers
math.NT2025
A truncated inner product formula in the geometry of numbers
Seokho Jin, Seungki Kim
We study the statistical distribution of primitive sublattices in the space of lattices . A central difficulty in this a…
math.NT2025
On counterexamples to the Mertens conjecture
Seungki Kim, Phong Q. Nguyen
We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to , which is significan…
math.NT2025
Bounds on the gaps in the fractional parts of a linear form
Seungki Kim
We provide bounds on the sizes of the gaps -- defined broadly -- in the set $\{k_1β_1 + \ldots + k_nβ_n \mbox{ (mod 1)} : k_i \in \mathbb Z \cap (0,Q^\frac{1}{n}]\}$ for generic…