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
HTML articles powered by AMS MathViewer

by Neal Koblitz

Trans. Amer. Math. Soc. 242 (1978), 261-269

DOI: https://doi.org/10.1090/S0002-9947-1978-0491622-3

PDF | 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

Emil Artin, The gamma function, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York-Toronto-London, 1964. Translated by Michael Butler. MR 0165148
Daniel Barsky, Introduction à l’analyse $p$-adique, Séminaire Delange-Pisot-Poitou (14e année: 1972/73), Théorie des nombres, Fasc. 2, Secrétariat Mathématique, Paris, 1973, pp. Exp. No. G2, 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

Kenkichi Iwasawa, Lectures on $p$-adic $L$-functions, Annals of Mathematics Studies, No. 74, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0360526, DOI 10.1515/9781400881703
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
M. Krasner, Rapport sur le prolongement analytique dans les corps valués complets par la méthode des éléments analytiques quasi-connexes, Table Ronde d’Analyse Non Archimédienne (Paris, 1972) Bull. Soc. Math. France, Mém. No. 39-40, Soc. Math. France, Paris, 1974, pp. 131–254 (French). MR 0385168, DOI 10.24033/msmf.166

Eine p-adische Theorie der Zetawerte

214/215

Analyse p-adique