À propos de la série ∑ n = 1 + ∞ x n q n - 1

Daniel Duverney

Journal de théorie des nombres de Bordeaux (1996)

  • Volume: 8, Issue: 1, page 173-181
  • ISSN: 1246-7405

How to cite

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Duverney, Daniel. "À propos de la série $\sum \limits _{n = 1}^{+ \infty } \frac{x^n}{q^n - 1}$." Journal de théorie des nombres de Bordeaux 8.1 (1996): 173-181. <http://eudml.org/doc/247825>.

@article{Duverney1996,
author = {Duverney, Daniel},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {linear independence over a field; irrationality; imaginary quadratic number field; Padé approximation},
language = {fre},
number = {1},
pages = {173-181},
publisher = {Université Bordeaux I},
title = {À propos de la série $\sum \limits _\{n = 1\}^\{+ \infty \} \frac\{x^n\}\{q^n - 1\}$},
url = {http://eudml.org/doc/247825},
volume = {8},
year = {1996},
}

TY - JOUR
AU - Duverney, Daniel
TI - À propos de la série $\sum \limits _{n = 1}^{+ \infty } \frac{x^n}{q^n - 1}$
JO - Journal de théorie des nombres de Bordeaux
PY - 1996
PB - Université Bordeaux I
VL - 8
IS - 1
SP - 173
EP - 181
LA - fre
KW - linear independence over a field; irrationality; imaginary quadratic number field; Padé approximation
UR - http://eudml.org/doc/247825
ER -

References

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  1. [1] K. Alladi and M.L. Robinson, Legendre Polynomials and Irrationality, J. Reine Angew. Math.318 (1980), 137-155. Zbl0425.10039MR579389
  2. [2] J.M. Arnaudiès, L'irréductibilité des polynômes cyclotomiques, R.M.S. (Octobre 1991). 
  3. [3] P.T. Bateman, Note on the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc.35 (1945), 1180-1181. Zbl0035.31102MR32677
  4. [4] J.P. Bézivin, Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire, Collect. Math.40, 1 (1989), 1-11. Zbl0708.11015MR1078087
  5. [5] P. Borwein, On the irrationality of Σ(1/(qn + r)), J. Number Theory37 (1991), 253-259. Zbl0718.11029
  6. [6] P. Borwein, On the irrationality of certain series, Math. Proc. Camb. Phil. Soc.112 (1992), 141-146. Zbl0779.11027MR1162938
  7. [7] P. Bundschuh, Ein Satz über ganze Funktionen und Irrationatätsaussagen, Inventiones Math.9 (1970), 175-184. Zbl0188.10801MR258758
  8. [8] P. Bundschuh and K. Väänänen, Arithmetical Investigations of a certain infinite product, Compositio Math.91 (1994), 175-201. Zbl0802.11027MR1273648
  9. [9] D. Duverney, Approximants de Padé et U-dérivation, Bull. Soc. Math. France122 (1994), 553-570. Zbl0810.05009MR1305669
  10. [10] P. Erdôs, On arithmetical properties of Lambert Series, J. Indian Math. Soc. (N.S.) 12 (1948), 63-66. Zbl0032.01701MR29405
  11. [11] G.H. Hardy and E.M. Wright, An introduction to the Theory of Numbers, Oxford Science Publications, Fifth Edition (1979). Zbl0423.10001MR568909
  12. [12] M. Mignotte, An Inequality about Irreducible Factors of Integer Polynomials, J. Number Theory30 (1988), 156-166. Zbl0648.12002MR961913

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