Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $ p$-adic log gamma function and $ p$-adic Euler constants


Author: Jack Diamond
Journal: Trans. Amer. Math. Soc. 233 (1977), 321-337
MSC: Primary 12B40; Secondary 33A15
MathSciNet review: 0498503
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)

  • [1] Jack Diamond, On the values of 𝑝-adic 𝐿-functions at positive integers, Acta Arith. 35 (1979), no. 3, 223–237. MR 550294 (80j:12013)
  • [2] Jean Fresnel, Nombres de Bernoulli et fonctions 𝐿 𝑝-adiques, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 2, 281–333 (1968) (French). MR 0224570 (37 #169)
  • [3] Kenkichi Iwasawa, Lectures on 𝑝-adic 𝐿-functions, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Annals of Mathematics Studies, No. 74. MR 0360526 (50 #12974)
  • [4] 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) Soc. Math. France, Paris, 1974, pp. 131–254. Bull. Soc. Math. France, Mém. No. 39–40 (French). MR 0385168 (52 #6033)
  • [5] Tomio Kubota and Heinrich-Wolfgang Leopoldt, Eine 𝑝-adische Theorie der Zetawerte. I. Einführung der 𝑝-adischen Dirichletschen 𝐿-Funktionen, J. Reine Angew. Math. 214/215 (1964), 328–339 (German). MR 0163900 (29 #1199)
  • [6] D. H. Lehmer, Euler constants for arithmetical progressions, Acta Arith. 27 (1975), 125–142. Collection of articles in memory of Juriĭ\ Vladimirovič Linnik. MR 0369233 (51 #5468)
  • [7] Y. Morita, A p-adic analog of the T function, (to appear).
  • [8] N. Nielsen, Die Gammafunktion, Bände I, II, Chelsea, New York, 1965. MR 32 #2622.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12B40, 33A15

Retrieve articles in all journals with MSC: 12B40, 33A15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0498503-9
PII: S 0002-9947(1977)0498503-9
Keywords: Log gamma function, Euler constants, p-adic functions
Article copyright: © Copyright 1977 American Mathematical Society