arXiv subjects

Junxuan Shen

Publications and source records attributed to Junxuan Shen.

2 recordsLinked to original sources

arXiv2023

Structural Szemerédi-Trotter for Lattices and their Generalizations

We completely characterize point--line configurations with $Θ(n^{4/3})$ incidences when the point set is a section of the integer lattice. This can be seen as the main special case of the structural Szemerédi-Trotter problem. We also derive a partial characterization for several generalizations: (i) We rule out the concurrent lines case when the point set is a Cartesian product of an arithmetic progression and an arbitrary set. (ii) We study the case of a Cartesian product where one or both sets are generalized arithmetic progression. Our proofs rely on deriving properties of multiplicative energies.

math.CO↗

arXiv2018

Optimal bounds for a Gaussian Arithmetic-Geometric type mean by quadratic and contraharmonic means

In this paper, we present the best possible parameters $α_i, β_i\ (i=1,2,3)$ and $α_4,β_4\in(1/2,1)$ such that the double inequalities \begin{align*} α_1Q(a,b)+(1-α_1)C(a,b)& 0$ with $a\neq b$, where $Q(a,b)$, $C(a,b)$ and $AG(a,b)$ are the quadratic, contraharmonic and Arithmetic-Geometric means, and $AG_{Q,C}(a,b)=AG[Q(a,b),C(a,b)]$. As consequences, we present new bounds for the complete elliptic integral of the first kind. Keywords: Arithmetic-Geometric mean, Complete elliptic integral, Quadratic mean, Contraharmonic mean

math.CA↗