For a certain class of hypergeometric functions $_{3}F_{2}$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.

中文翻译：

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超几何函数特殊值的代数几何研究

对于某类超几何函数$_{3}F_{2}$使用有理参数，我们给出了特殊值的充分条件$1$用代数数的对数表示。我们给出了两个证明，这两个证明都是代数几何的，并且都与更高的监管者有关。