Senping Luo

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20242026

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math.AP2025

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…

math.AP2024

A new type of minimizers in lattice energy and its application

Kaixin Deng, Senping Luo

Let $z \in H := {z = x + i y \in C : y > 0}$ and $\mathcal{K}(Î±;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-ÏÎ±\frac{ \left|mz+n\ri…

math.AP2024

Minimizing Lattice Energy and Hexagonal Crystallization

Kaixin Deng, Senping Luo

Consider the energy per particle on the lattice given by $min_{I^} \sum_{P \in I^} ∣ P ∣^{4} e^{- I ¨ I^\pm ∣ P ∣^{2}}$ , where $I^\pm > 0$ and $I^$ i…