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<p>Using Appell function properties we give short proofs of Ramanujan-like identities for the eighth order mock theta function <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1139_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(V_0(q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>V</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> after work of Chan and Mao; Mao; and Brietzke, da Silva, and Sellars. We also present a generalization of the identities in the spirit of celebrated results of Bringmann, Ono, and Rhoades on Dyson’s ranks and Maass forms.</p>

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Short proofs of Ramanujan-like identities for the eighth order mock theta function \(V_{0}(q)\)

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Eric T. Mortenson

摘要

Using Appell function properties we give short proofs of Ramanujan-like identities for the eighth order mock theta function \(V_0(q)\) V 0 ( q ) after work of Chan and Mao; Mao; and Brietzke, da Silva, and Sellars. We also present a generalization of the identities in the spirit of celebrated results of Bringmann, Ono, and Rhoades on Dyson’s ranks and Maass forms.