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arXiv · 2205.00649

On the period interpretation for some special values of Thakur hypergeometric functions

Ryotaro Harada
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Abstract

In 1995, Thakur invented and studied positive characteristic analogues of hypergeometric functions. In this paper, we interpret the special values of those functions as periods of a pre-$t$-motive. As a consequence, we show their transcendence and linear independence results by using Chang's refined version of the Anderson-Brownawell-Papanikolas criterion. Furthermore, as by-products, we show some linear/algebraic independence results among the special values of Kochubei multiple polylogarithms according to our period interpretation and the corresponding refined criterion.

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Ryotaro Harada. 2022-05-02. On the period interpretation for some special values of Thakur hypergeometric functions. https://arxiv.org/abs/2205.00649

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