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<p>Determining the explicit forms and modularity for string functions and branching coefficients for Kac–Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac–Moody algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_{1}^{(1)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>A</mi> <mrow> <mn>1</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>. For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained mixed false theta function expressions. Here we find two new families of mock theta conjecture-like identities but for the 2/5-level string functions. Each of these two families of identities is composed of the four tenth-order mock theta functions from Ramanujan’s Lost Notebook as well as a simple quotient of theta functions.</p>

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Two 2/5-level mock theta conjecture-like identities

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Stepan Konenkov,
  • Eric T. Mortenson

摘要

Determining the explicit forms and modularity for string functions and branching coefficients for Kac–Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac–Moody algebra \(A_{1}^{(1)}\) A 1 ( 1 ) . For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained mixed false theta function expressions. Here we find two new families of mock theta conjecture-like identities but for the 2/5-level string functions. Each of these two families of identities is composed of the four tenth-order mock theta functions from Ramanujan’s Lost Notebook as well as a simple quotient of theta functions.