Interpretation of the 𝑝-adic log gamma function and Euler constants using the Bernoulli measure

Koblitz, Neal

doi:10.1090/S0002-9947-1978-0491622-3

Interpretation of the $p$-adic log gamma function and Euler constants using the Bernoulli measure
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Trans. Amer. Math. Soc. 242 (1978), 261-269 Request permission

Abstract:

A regularized version of J. Diamond’s p-adic log gamma function and his p-adic Euler constants are represented as integrals using B. Mazur’s p-adic Bernoulli measure.

References

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Daniel Barsky, Introduction à l’analyse $p$-adique, Séminaire Delange-Pisot-Poitou, 14e année (1972/73), Theorie des nombres, Fasc. 2, Exp. No. G2, Secrétatiat Mathèmatique, Paris, 1973, pp. 2 (French). MR 0389832
Jack Diamond, The $p$-adic log gamma function and $p$-adic Euler constants, Trans. Amer. Math. Soc. 233 (1977), 321–337. MR 498503, DOI 10.1090/S0002-9947-1977-0498503-9

On the values of p-adic L-functions at positive integers

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Neal Koblitz, $p$-adic numbers, $p$-adic analysis, and zeta-functions, Graduate Texts in Mathematics, Vol. 58, Springer-Verlag, New York-Heidelberg, 1977. MR 0466081, DOI 10.1007/978-1-4684-0047-2
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Eine p-adische Theorie der Zetawerte

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Analyse p-adique