Dedekind η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-function identities of level 6 and an approach towards colored partitions

被引：0
作者：
B. R. Srivatsa Shruthi
机构：
[1] Manipal Academy of Higher Education,Department of Mathematics, Manipal Institute of Technology
来源：
Boletín de la Sociedad Matemática Mexicana | 2021年 / 27卷 / 3期
关键词：
Colored partitions; Dedekind ; -function; Modular equations; Theta functions; Primary 11P83; Secondary 05A15; 05A17;
D O I：
10.1007/s40590-021-00389-1
中图分类号：
学科分类号：
摘要：
Somos conjectured thousands of Dedekind η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-function identities of various levels, around 6200 in number. He did so using computational evidence but has not sought to provide any proof for these identities. In this paper, we prove level 6 of Somos’s Dedekind η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-function identities containing five terms in two methods. Further, as an application of these identities, we deduce colored partitions for the same.
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