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On transformation formulas of $p$-adic hypergeometric functions
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abstract
In this paper, we review hypergeometric functions $\mathscr{F}^{\rm Dw}_{\underline{a}}(t),$ $\mathscr{F}^{(\sigma)}_{\underline{a}}(t)$ and $\widehat{\mathscr{F}}^{(\sigma)} _{\mathbf{a}}(t)$ together with their conjectured transformation formulas, and show that one transformation formula implies the other.
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Transformation formula of Dwork's $p$-adic hypergeometric function
For a in N^{-1}Z with p not dividing N and 0<a<1, Dwork's p-adic hypergeometric function satisfies F(t)=((-1)^(d+1)t)^l F(t^{-1}) for all d, with a precise sign rule when p=2.
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