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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$p$-adic gamma functions and Dwork cohomology


Author: Maurizio Boyarsky
Journal: Trans. Amer. Math. Soc. 257 (1980), 359-369
MSC: Primary 12B40; Secondary 10Gxx, 12H25
DOI: https://doi.org/10.1090/S0002-9947-1980-0552263-1
MathSciNet review: 552263
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Abstract: The relations of Gross and Koblitz between gauss sums and the p-adic gamma function is reexamined from the point of view of Dwork’s formulation of p-adic cohomology. Some higher dimensional generalizations are proposed.


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

    P. G. Lejeune Dirichlet, J. Reine Angew. Math. 15 (1836), 258-263.
  • Bernard Dwork, On the zeta function of a hypersurface. II, Ann. of Math. (2) 80 (1964), 227–299. MR 188215, DOI https://doi.org/10.2307/1970392
  • B. Dwork, $p$-adic cycles, Inst. Hautes Études Sci. Publ. Math. 37 (1969), 27–115. MR 294346
  • B. Dwork, Bessel functions as $p$-adic functions of the argument, Duke Math. J. 41 (1974), 711–738. MR 387281
  • H. Davenport and H. Hasse, Die Nullstellen der Knogruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1934), 151-182.
  • Yasuo Morita, A $p$-adic analogue of the $\Gamma $-function, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975), no. 2, 255–266. MR 424762
  • N. Sonine, Bull. Soc. Math. France 9 (1880), 162-166.

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Keywords: <I>p</I>-adic, gamma function, <I>p</I>-adic cohomology, Washnitzer-Monsky cohomology
Article copyright: © Copyright 1980 American Mathematical Society