On a mixed Littlewood conjecture for quadratic numbers

Bernard de Mathan[1]

  • [1] Université Bordeaux I UFR Math-Info. Laboratoire A2X 351 cours de la Libération 33405 Talence, France

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 207-215
  • ISSN: 1246-7405

Abstract

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We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in p -adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.

How to cite

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de Mathan, Bernard. "On a mixed Littlewood conjecture for quadratic numbers." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 207-215. <http://eudml.org/doc/249462>.

@article{deMathan2005,
abstract = {We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in $ p$-adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.},
affiliation = {Université Bordeaux I UFR Math-Info. Laboratoire A2X 351 cours de la Libération 33405 Talence, France},
author = {de Mathan, Bernard},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {207-215},
publisher = {Université Bordeaux 1},
title = {On a mixed Littlewood conjecture for quadratic numbers},
url = {http://eudml.org/doc/249462},
volume = {17},
year = {2005},
}

TY - JOUR
AU - de Mathan, Bernard
TI - On a mixed Littlewood conjecture for quadratic numbers
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 207
EP - 215
AB - We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in $ p$-adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.
LA - eng
UR - http://eudml.org/doc/249462
ER -

References

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  1. M. Bauer, M. Bennett, Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270. Zbl1010.11020MR1908198
  2. Y. Bugeaud, M. Laurent, Minoration effective de la distance p -adique entre puissances de nombres algébriques. J. Number Theory 61 (1996), 311–342. Zbl0870.11045MR1423057
  3. B. de Mathan, Linear forms in logarithms and simultaneous Diophantine approximation. (To appear). Zbl1195.11086
  4. B. de Mathan, Approximations diophantiennes dans un corps local. Bull. Soc. math. France, Mémoire 21 (1970). Zbl0221.10037MR274396
  5. B. de Mathan, O. Teulié, Problèmes diophantiens simultanés. Monatshefte Math. 143 (2004), 229–245. Zbl1162.11361MR2103807
  6. D. Ridout, Rational approximations to algebraic numbers. Mathematika 4 (1957), 125–131. Zbl0079.27401MR93508
  7. L. G. Peck, Simultaneous rational approximations to algebraic numbers. Bull. Amer. Math. Soc. 67 (1961), 197–201. Zbl0098.26302MR122772
  8. K. Yu, p -adic logarithmic forms and group varieties II. Acta Arith. 89 (1999), 337–378. Zbl0928.11031MR1703864

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