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On Morita's p-adic gamma function

Published online by Cambridge University Press:  24 October 2008

Daniel Barsky
Daniel Barsky
Affiliation:
U.E.R. de Mathématiques, Paris
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Extract

Y. Morita proved that, for each prime number p, one can define a p-adic continuous function Γp(x) from p to p, interpolating the sequence

where m runs through the integers m prime to p with 1 ≤ m < n. Our aim is to show how this result is related to Dwork's result on the radius of convergence of

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 23 - 27
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

(1)Amice, Y.Interpolation p-adique. Bull. Soc. Math. France, 92 (1964), pp. 117–180 (Thèse Sc. Math., Paris 1964).CrossRefGoogle Scholar
(2)Amice, Y.Les nombres p-adiques (Paris, Presses Universitaires de France, 1975: Collection Sup., ‘Le Mathématicien’, 14).Google Scholar
(3)Barsky, D.Transformation de Cauchy p-adique et algèbre d'Iwasawa. Math. Annalen 232 (1978), 255–266.CrossRefGoogle Scholar
(4)Boyarsky, B.p-adic gamma function and Dwork cohomology. Trans. Amer. Math. Soc. 257 (1980), 359–369.Google Scholar
(5)Diamond, J. On the value of p-adic L functions at positive integers (to appear).Google Scholar
(6)Dwork, B.On the rationality of the zeta function of an algebraic variety. Amer. J. of Math. 82 (1960), 631–648.CrossRefGoogle Scholar
(7)Gross, B. and Koblitz, N.Gauss sums and the p-adic Γ function. Annals of Math. 109 (1979), 569–581.CrossRefGoogle Scholar
(8)Katz, N. Graduate course, at Princeton University, spring 1978.Google Scholar
(9)Monsky, P.p-adic analysis and zeta function. Tokyo, Kinokuniya Bookstore, 1970 (Lectures in Math.; Kyoto University, 4).Google Scholar
(10)Morita, Y.A p-adic analogue of the Γ-function. J. Fac. Sc. University Tokyo, section 1, 22 (1975), 255–266.Google Scholar