Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Fixed points of the $ {p}$-adic $ {q}$-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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The $ q$-bracket $ [X]_q:\textrm{O}_{\mathbb{C}_p}\to\textrm{O}_{\mathbb{C}_p}$, which is the $ q$-analog of the identity function, is also a norm-preserving isometry, for each $ q\in \textrm{B}(1,p^{-1/(p-1)})$. In this paper we investigate its fixed points.


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

  • [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 $ p$-adic numbers, J. Ramanujan Math. Soc. 8 (1993), no. 1-2, 1-5. MR 1236398 (94f:11124)
  • [C] Conrad, K.: A $ q$-analogue of Mahler expansions. I, Adv. Math. 153 (2000), no. 2, 185-230. MR 1770929 (2001i:11140)
  • [D] Dieudonné, J.: Sur les fonctions continues $ p$-adiques, Bull. Sci. Math. (2) 68 (1944), 79-95. MR 0013142 (7:111c)
  • [F] Fray, R. D.: Congruence properties of ordinary and $ q$-binomial coefficients, Duke Math. J. 34 (1967), 467-480. MR 0213287 (35:4151)
  • [G] F. Q. Gouvêa, $ p$-adic Numbers, an Introduction, Second edition, Springer-Verlag, New York, 2003. MR 1488696 (98h:11155)
  • [J] Jackson, F. H.: $ q$-difference equations, Amer. J. Math. 32 (1910), 305-314. MR 1506108
  • [M] Mahler, K.: An interpolation series for continuous functions of a $ p$-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 $ p$-adic integers, Visnik Kiïv. Univ. Ser. Mat. Mekh. 117, no. 30 (1988), 100-107. MR 1004462 (90k:11160)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11B65, 11S80, 26E30, 12J25

Retrieve articles in all journals with MSC (2010): 11B65, 11S80, 26E30, 12J25


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.

American Mathematical Society