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The $p$-Adic Log Gamma Function and $p$-Adic Euler Constants

Jack Diamond
Transactions of the American Mathematical Society
Vol. 233 (Oct., 1977), pp. 321-337
DOI: 10.2307/1997840
Stable URL: http://www.jstor.org/stable/1997840
Page Count: 17
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The $p$-Adic Log Gamma Function and $p$-Adic Euler Constants
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Abstract

We define $G_p$, a $p$-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define $p$-adic Euler constants and use them to obtain results on $G'_p$ and on the logarithmic derivative of Morita's $\Gamma_p$.

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