Geodesic
$t$-motivic interpretations for special values of Thakur hypergeometric functions and Kochubei multiple polylogarithms
Documenta mathematica, Tome 30 (2025) no. 3, pp. 673-707

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In 1995, Thakur invented and studied positive characteristic analogues of hypergeometric functions. In this paper, we interpret the special values of those functions by rigid analytic trivializations for some pre-t-motives. As a consequence, we show their transcendence and linear independence results by using Chang’s refined version of the Anderson–Brownawell–Papanikolas criterion. Furthermore, we show some linear independence results among the special values of Kochubei multiple polylogarithms according to our t-motivic interpretation and the corresponding refined criterion.
DOI : 10.4171/dm/1004
Classification : 11J93, 11M38, 11J72, 11J91
Mots-clés : hypergeometric functions in positive characteristic, multiple polylogarithms in positive characteristic, pre-t-motives, linear independence 
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     author = {Ryotaro Harada},
     title = {$t$-motivic interpretations for special values of {Thakur} hypergeometric functions and {Kochubei} multiple polylogarithms},
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Ryotaro Harada. $t$-motivic interpretations for special values of Thakur hypergeometric functions and Kochubei multiple polylogarithms. Documenta mathematica, Tome 30 (2025) no. 3, pp. 673-707. doi: 10.4171/dm/1004

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