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Lehmer $ k$-tuples


Authors: Emre Alkan, Florin Stan and Alexandru Zaharescu
Journal: Proc. Amer. Math. Soc. 134 (2006), 2807-2815
MSC (2000): Primary 11L05, 11K36
DOI: https://doi.org/10.1090/S0002-9939-06-08484-X
Published electronically: April 10, 2006
MathSciNet review: 2231602
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Abstract: Generalizing a classical problem of Lehmer, in this paper we provide an asymptotic result for the number of Lehmer $ k$-tuples.


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

  • 1. C. Cobeli, A. Zaharescu, Generalization of a problem of Lehmer, Manuscripta Math. 104 (2001), no. 3, 301-307. MR 1828876 (2003a:11100)
  • 2. R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, Berlin (1981) (second edition 1994). MR 1299330 (96e:11002)
  • 3. H. Davenport, On a principle of Lipschitz, J. London Math. Soc. 26 (1951), 179-183. MR 0043821 (13:323d)
  • 4. P. Deligne, Seminaire Geometrie Algebrique 4$ \frac12$, Lecture Notes 569 (1977), 221-228. MR 0463174 (57:3132)
  • 5. R. A. Smith, On $ n$-dimensional Kloosterman sums, J. Number Theory 11 (1979), 324-343. MR 0544261 (80i:10052)
  • 6. R. A. Smith, A generalization of Kuznietsov's identity for Kloosterman sums, C. R. Math. Rep. Acad. Sci. Canada Vol. II (1980), 315-320.MR 0600568 (82j:10068)
  • 7. A. Weil, On some exponential sums, Proc Nat.Acad.Sci. U.S.A. 34 (1948), 204-207. MR 0027006 (10:234e)
  • 8. L. Weinstein, The hyper-Kloosterman sum, Enseign. Math. (2) 27 (1981), no. 1-2, 29-40. MR 0630958 (83b:10046)
  • 9. W. Zhang, On a problem of D. H. Lehmer and its generalization, Compositio Math. 86 (1993), no. 3, 307-316. MR 1219630 (94f:11104)
  • 10. W. Zhang, A problem of D. H. Lehmer and its generalization II, Compositio Math. 91 (1994), no. 1, 47-56. MR 1273925 (95f:11079)
  • 11. W. Zhang, On the difference between a D. H. Lehmer number and its inverse modulo $ q,$ Acta Arith. 68 (1994), no. 3, 255-263. MR 1308126 (96a:11100)

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Additional Information

Emre Alkan
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
Email: alkan@math.uiuc.edu

Florin Stan
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania – and – Department of Mathematics, University of Illinois at Urbana- Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
Email: fstan@math.uiuc.edu

Alexandru Zaharescu
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania – and – Department of Mathematics, University of Illinois at Urbana- Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
Email: zaharesc@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08484-X
Keywords: Lehmer numbers, uniform distribution, Hyper-Kloosterman sums
Received by editor(s): April 18, 2005
Published electronically: April 10, 2006
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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