Author:
Kaur Harman,Rana Meenakshi
Abstract
<p style='text-indent:20px;'>Ramanujan introduced sixth order mock theta functions <inline-formula><tex-math id="M3">\begin{document}$ \lambda(q) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \rho(q) $\end{document}</tex-math></inline-formula> defined as:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \lambda(q) & = \sum\limits_{n = 0}^{\infty}\frac{(-1)^n q^n (q;q^2)_n}{(-q;q)_n},\\ \rho(q) & = \sum\limits_{n = 0}^{\infty}\frac{ q^{n(n+1)/2} (-q;q)_n}{(q;q^2)_{n+1}}, \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>listed in the Lost Notebook. In this paper, we present some Ramanujan-like congruences and also find their infinite families modulo 12 for the coefficients of mock theta functions mentioned above.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference8 articles.
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1 articles.
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