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arXiv · 1702.04200

A distribution formula for Kashio's $p$-adic log-gamma function

Eugenio Finat
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Abstract

We study a special case of Kashio's $p$-adic $\logΓ$-function, that we call ${\mathrm{Log}}Γ_{\mathit{p}}$, which combines these of Morita and Diamond. It agrees with each of these on large parts of its domain and has the advantage of being a locally analytic function. We prove a distribution formula for ${\mathrm{Log}}Γ_{\mathit{p}}$ which generalizes and links the known distribution formulas for Diamond's and Morita's functions.

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Eugenio Finat. 2017-02-14. A distribution formula for Kashio's $p$-adic log-gamma function. https://doi.org/10.1016/j.jnt.2015.11.001

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