On ratios of theta functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913102653554688 |
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| author | Luo, Senping Wei, Juncheng |
| author_facet | Luo, Senping Wei, Juncheng |
| contents | 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 space $($Maloney-Witten \cite{Witten2020}$)$, we investigate ratios of theta functions. In this paper, we completely classify the minimizers (or maximizers) for ratios of theta and Epstein zeta functions. We find that the hexagonal lattice plays a pivotal role there. These results have direct applications in conformal and Liouville field theory via partition functions. Additionally, they yield the minima of differences of theta and Epstein zeta functions, which have implications for the mathematics of crystallization and interacting particle theory (\cite{Bet2016,Bet2019AMP}). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07580 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On ratios of theta functions Luo, Senping Wei, Juncheng Classical Analysis and ODEs Mathematical Physics Analysis of PDEs Complex Variables Number Theory 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 space $($Maloney-Witten \cite{Witten2020}$)$, we investigate ratios of theta functions. In this paper, we completely classify the minimizers (or maximizers) for ratios of theta and Epstein zeta functions. We find that the hexagonal lattice plays a pivotal role there. These results have direct applications in conformal and Liouville field theory via partition functions. Additionally, they yield the minima of differences of theta and Epstein zeta functions, which have implications for the mathematics of crystallization and interacting particle theory (\cite{Bet2016,Bet2019AMP}). |
| title | On ratios of theta functions |
| topic | Classical Analysis and ODEs Mathematical Physics Analysis of PDEs Complex Variables Number Theory |
| url | https://arxiv.org/abs/2605.07580 |