6 citations · 15 across the 11 of their papers we have counts for
12 papers
Explicit second moments of symplectic Siegel transforms
Kristian Holm, Seungki Kim
We give two alternate formulations for the second moment formula of the Siegel transform over , originally establ…
A new upper bound on the smallest counterexample to the Mertens conjecture
John Rozmarynowycz, Seungki Kim
We report the finding of the new upper bound on the lowest positive integer for which the Mertens conjecture \begin{equation*} \left| \sum_{1 \leq n \leq x} μ(n) \right| < \sqr…
Adelic Rogers integral formula
Seungki Kim
We formulate and prove the extension of the Rogers integral formula to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a n…
Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices
Seungki Kim, Mishel Skenderi
We prove a higher-rank analogue of a well-known result of W. M. Schmidt concerning almost everywhere pointwise discrepancy bounds for lattices in Euclidean space (see Theorem 1 [Tr…
A physical study of the LLL algorithm
Jintai Ding, Seungki Kim, Tsuyoshi Takagi +2
This paper presents a study of the LLL algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting LLL as…
Mean value formulas on sublattices and flags of the random lattice
Seungki Kim
We present the extensions of the Siegel integral formula ([10]), which counts the vectors of the random lattice, to the context of counting its sublattices and flags. Perhaps surpr…
Counting rational points on a Grassmannian
Seungki Kim
We prove an estimate on the number of rational points on the Grassmannian variety of bounded twisted height, refining the classical results of Schmidt ([12]) and Thunder ([20]) ove…
A stochastic variant of the abelian sandpile model
Seungki Kim, Yuntao Wang
We introduce a natural stochastic extension, called SSP, of the abelian sandpile model(ASM), which shares many mathematical properties with ASM, yet radically differs in its physic…
LLL and stochastic sandpile models
Jintai Ding, Seungki Kim, Tsuyoshi Takagi +1
Theaimofthepresentpaperistosuggestthatstatisticalphysicsprovides the correct language to understand the practical behavior of the LLL algorithm, most of which are left unexplained…
Random lattice vectors in a set of size O(n)
Seungki Kim
We adopt the sieve ideas of Schmidt and Södergren in order to study the statistics of vectors of a random lattice of dimension n contained in a set of volume O(n). We also give som…
The behavior of random reduced bases
Seungki Kim, Akshay Venkatesh
We prove that the number of Siegel-reduced bases for a randomly chosen -dimensional lattice becomes, for , tightly concentrated around its mean. We also sh…
On the distribution of lengths of short vectors in a random lattice
Seungki Kim
We use an idea from sieve theory to estimate the distribution of the lengths of th shortest vectors in a random lattice of covolume 1 in dimension . This is an improvement of…