11 citations · 29 across the 12 of their papers we have counts for
13 papers
On Sarnak--Strömbergsson conjecture
Senping Luo, Juncheng Wei
Let $\Th(α,L)=\sum_{v\in L}e^{-πα|v|^2}$ for and for be the theta and Epstein zeta functions associated to the lattice $…
On ratios of theta functions
Senping Luo, Juncheng Wei
Motivated by the average partition function of c free bosons Afhkami-Jeddi et al. \cite{Afhk2021} and the average of the genus 1 partition function over the Narain moduli spa…
Signs of high order derivatives for the theta and Epstein zeta functions and application
Deng Kaixin, Luo Senping
In the 1950s, 1960s and 1988, number theorists Rankin \cite{Ran1953}, Cassels \cite{Cas1959}, Ennola \cite{Enn1964a}, Diananda \cite{Dia1964}, and Montgomery \cite{Mon1988} derived…
A new type of minimizers in lattice energy and its application
Kaixin Deng, Senping Luo
Let and $\mathcal{K}(α;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-πα\frac{ \left|mz+n\right…
Minimizing Lattice Energy and Hexagonal Crystallization
Kaixin Deng, Senping Luo
Consider the energy per particle on the lattice given by , where and is a tw…
On a variational model for the continuous mechanics exhibiting hexagonal to square Phase Transitions
Senping Luo, Juncheng Wei
Inspired by Conti and Zanzotto \cite{Conti2004A}, we reformulate a simple variational model for reconstructive phase transitions in crystals arising in continuum mechanics in the f…
On lattice hexagonal crystallization for non-monotone potentials
Senping Luo, Juncheng Wei
Let where be the two dimensional lattices…
On Minima of Difference of Epstein Zeta Functions and Exact Solutions to Lennard-Jones Lattice Energy
Senping Luo, Juncheng Wei
Let be the Eisenstein series/Epstein Zeta function. Motivated by widely used Lennard-Jones potenti…
On minima of sum of theta functions and Mueller-Ho Conjecture
Senping Luo, Juncheng Wei
Let and be the theta function associated with the lattic…
On finite Morse index solutions to the quadharmonic Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic Lane-Emden equation, derive a monotonicity formula and classify the finite Morse index solution to the f…
Classification of the stable solution to the fractional Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
We classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: in for .
Existence, nonexistence, symmetry and uniqueness of ground state for critical Schrödinger system involving Hardy term
Senping Luo, Wenming Zou
We study the following elliptic system with critical exponent: \begin{displaymath} \begin{cases}-Δu_j-\frac{λ_j}{|x|^2}u_j=u_j^{2^*-1}+\sum\limits_{k\neq j}β_{jk}α_{jk}u_j^{α_{jk}-…
On the triharmonic Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \begin{equat…