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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.09201 |
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Table of Contents:
- Let $z\in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\mathcal{K}(α;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-πα\frac{ \left|mz+n\right|^2}{\Im(z)}}.$ In this paper, we characterize the following minimization problem$:$ $\min_{ \mathbb{H} } \big(\mathcal{K}(α;z)-b\mathcal{K}(2α;z)\big).$ We prove that there exist hexagonal to skinny-rhombic minimizers, which is a novel finding in the literature.