Generalized p-adic hypergeometric functions of logarithmic type are introduced, shown to obey congruence relations like prior work, and proven to have zero special values at t=1 under certain conditions.
Kato,Logarithmic structures of Fontaine-Illusie, Johns Hopkins University Press, Balti- more, MD, 1989, 191–224
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On special values of generalized $p$-adic hypergeometric functions of logarithmic type
Generalized p-adic hypergeometric functions of logarithmic type are introduced, shown to obey congruence relations like prior work, and proven to have zero special values at t=1 under certain conditions.