The metric simultaneous diophantine approximations over formal power series

Kae Inoue

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 151-161
  • ISSN: 1246-7405

Abstract

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We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.

How to cite

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Inoue, Kae. "The metric simultaneous diophantine approximations over formal power series." Journal de théorie des nombres de Bordeaux 15.1 (2003): 151-161. <http://eudml.org/doc/249091>.

@article{Inoue2003,
abstract = {We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.},
author = {Inoue, Kae},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {1},
pages = {151-161},
publisher = {Université Bordeaux I},
title = {The metric simultaneous diophantine approximations over formal power series},
url = {http://eudml.org/doc/249091},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Inoue, Kae
TI - The metric simultaneous diophantine approximations over formal power series
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 151
EP - 161
AB - We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.
LA - eng
UR - http://eudml.org/doc/249091
ER -

References

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  1. [1] R.J. Duffin, A.C. Schaeffer, Khintchine's problem in metric diophantine approximation. Duke Math. J.8 (1941), 243-255. Zbl0025.11002MR4859JFM67.0145.03
  2. [2] G.W. Effinger, D.R. Hayes, Additive Number Theory of Polynomials Over a Finite Field. Oxford University Press, New York, 1991. Zbl0759.11032MR1143282
  3. [3] P.X. Gallagher, Approximation by reduced fractions. J. Math. Soc. Japan13 (1961), 342-345. Zbl0106.04106MR133297
  4. [4] K. Inoue, H. Nakada, On metric Diophantine approximation in positive characteristic, preprint. Zbl1049.11073MR2008007
  5. [5] M.G. Nadkarni, Basic Ergodic Theory. Birkäuser Verlag, Basel-Boston- Berlin, 1991. MR1725389
  6. [6] A.D. Pollington, R.C. Vaughan, The k-dimensional Duffin and Shaeffer conjecture. Sém. Théor. Nombres Bordeaux1 (1989), 81-87. Zbl0714.11048MR1050267
  7. [7] M. Rosen, Number Theory in Function Fields. Springer-Verlag, New York-Berlin-Heidelberg, 2001. Zbl1043.11079MR1876657
  8. [8] V.G. Sprindżuk, Metric Theory of Diophantine Approximations. John Wiley & Sons, New York -Toronto-London- Sydney, 1979. Zbl0482.10047MR548467

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