Fixed points of the -adic -bracket

Author:
Eric Brussel

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1501-1511

MSC (2010):
Primary 11B65, 11S80; Secondary 26E30, 12J25

DOI:
https://doi.org/10.1090/S0002-9939-2011-11012-8

Published electronically:
August 19, 2011

MathSciNet review:
2869135

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Abstract | References | Similar Articles | Additional Information

Abstract: The -bracket , which is the -analog of the identity function, is also a norm-preserving isometry, for each . In this paper we investigate its fixed points.

**[A]**Arens, R.:*Homeomorphisms preserving measure in a group*, Ann. of Math. (2),**60**, no. 3 (1954), pp. 454-457. MR**0064061 (16:220b)****[B]**Bishop, E.:*Isometries of the -adic numbers*, J. Ramanujan Math. Soc.**8**(1993), no. 1-2, 1-5. MR**1236398 (94f:11124)****[C]**Conrad, K.:*A -analogue of Mahler expansions. I,*Adv. Math.**153**(2000), no. 2, 185-230. MR**1770929 (2001i:11140)****[D]**Dieudonné, J.:*Sur les fonctions continues -adiques*, Bull. Sci. Math. (2)**68**(1944), 79-95. MR**0013142 (7:111c)****[F]**Fray, R. D.:*Congruence properties of ordinary and -binomial coefficients,*Duke Math. J.**34**(1967), 467-480. MR**0213287 (35:4151)****[G]**F. Q. Gouvêa,*-adic Numbers, an Introduction*, Second edition, Springer-Verlag, New York, 2003. MR**1488696 (98h:11155)****[J]**Jackson, F. H.:*-difference equations*, Amer. J. Math.**32**(1910), 305-314. MR**1506108****[M]**Mahler, K.:*An interpolation series for continuous functions of a -adic variable*, J. Reine Angew. Math.**199**(1958), 23-34. MR**0095821 (20:2321)****[Se]**Serre, J-P.:*Lie Algebras and Lie Groups*, Lecture Notes in Math., 1500, Springer-Verlag, New York, 1992. MR**1176100 (93h:17001)****[Su]**Sushchanskiĭ, V. I.:*Standard subgroups of the isometry group of the metric space of -adic integers*, Visnik Kiïv. Univ. Ser. Mat. Mekh.**117**, no. 30 (1988), 100-107. MR**1004462 (90k:11160)**

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Additional Information

**Eric Brussel**

Affiliation:
Department of Mathematics, Emory University, Atlanta, Georgia 30322

DOI:
https://doi.org/10.1090/S0002-9939-2011-11012-8

Received by editor(s):
January 11, 2011

Published electronically:
August 19, 2011

Communicated by:
Matthew A. Papanikolas

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.