We characterize Zagier’s generating series of extended period polynomials of normalized Hecke eigenforms for \({{\,\mathrm{PSL}\,}}_2(\mathbb {Z})\) in terms of the period relations and existence of a suitable factorization. For this, we prove a characterization of the Kronecker function as the “fundamental solution” of the Fay identity.

中文翻译：

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Kronecker函数的代数表征

我们根据周期关系和适当的存在性来表征Zagier为\（{{\，\ mathrm {PSL} \，}} _ 2（\ mathbb {Z}）\）归一化的Hecke特征形生成的一系列扩展周期多项式因式分解。为此，我们证明了Kronecker函数是Fay身份的“基本解决方案”的特征。