Congruences modulo 4 and 8 for Ramanujan’s sixth-order mock theta function ρ(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho (q)$$\end{document}Congruences modulo 4 and 8 for Ramanujan’s sixth-order...Y. Hu etal.

被引：0

作者：

Yueya Hu ^{[1
]}

Eric H. Liu ^{[2
]}

Olivia X. M. Yao ^{[1
]}

机构：

[1] Suzhou University of Science and Technology,School of Mathematical Sciences

[2] Shanghai University of International Business and Economics,School of Statistics and Information

来源：

The Ramanujan Journal | 2025年 / 66卷 / 4期

关键词：

Congruences; Ramanujan’s mock theta functions; Class number; 11P83; 05A17;

D O I：

10.1007/s11139-024-01018-x

中图分类号：

学科分类号：

摘要：

Recently, Wang gave a systematic study on the parity of coefficients of classical mock theta functions. Very recently, Chen and Garvan proved some congruences modulo 4 for five of Ramanujan’s mock theta functions. Kaur and Rana studied congruences for Ramanujan’s sixth-order mock theta function ρ(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho (q)$$\end{document} in the arithmetic progressions 2n. In this paper, we prove some new congruences modulo 4 and 8 for ρ(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho (q)$$\end{document} in the arithmetic progressions 2n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2n+1$$\end{document} by using some results on the Hurwitz class number due to Chen and Garvan and an identity proved by Mortenson.

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