@article{JTNB_1996__8_1_173_0, author = {Duverney, Daniel}, title = {\`A propos de la s\'erie $\sum \limits _{n = 1}^{+ \infty } \frac{x^n}{q^n - 1}$}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {173--181}, publisher = {Universit\'e Bordeaux I}, volume = {8}, number = {1}, year = {1996}, mrnumber = {1399953}, zbl = {0867.11054}, language = {fr}, url = {http://www.numdam.org/item/JTNB_1996__8_1_173_0/} }
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 SP - 173 EP - 181 VL - 8 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1996__8_1_173_0/ LA - fr ID - JTNB_1996__8_1_173_0 ER -
%0 Journal Article %A Duverney, Daniel %T À propos de la série $\sum \limits _{n = 1}^{+ \infty } \frac{x^n}{q^n - 1}$ %J Journal de théorie des nombres de Bordeaux %D 1996 %P 173-181 %V 8 %N 1 %I Université Bordeaux I %U http://www.numdam.org/item/JTNB_1996__8_1_173_0/ %G fr %F JTNB_1996__8_1_173_0
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, Tome 8 (1996) no. 1, pp. 173-181. http://www.numdam.org/item/JTNB_1996__8_1_173_0/
[1] Legendre Polynomials and Irrationality, J. Reine Angew. Math. 318 (1980), 137-155. | MR | Zbl
and ,[2] L'irréductibilité des polynômes cyclotomiques, R.M.S. (Octobre 1991).
,[3] Note on the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 35 (1945), 1180-1181. | MR | Zbl
,[4] Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire, Collect. Math. 40, 1 (1989), 1-11. | MR | Zbl
,[5] On the irrationality of Σ(1/(qn + r)), J. Number Theory 37 (1991), 253-259. | Zbl
,[6] On the irrationality of certain series, Math. Proc. Camb. Phil. Soc. 112 (1992), 141-146. | MR | Zbl
,[7] Ein Satz über ganze Funktionen und Irrationatätsaussagen, Inventiones Math. 9 (1970), 175-184. | MR | Zbl
,[8] Arithmetical Investigations of a certain infinite product, Compositio Math. 91 (1994), 175-201. | Numdam | MR
and ,[9] Approximants de Padé et U-dérivation, Bull. Soc. Math. France 122 (1994), 553-570. | Numdam | MR | Zbl
,[10] On arithmetical properties of Lambert Series, J. Indian Math. Soc. (N.S.) 12 (1948), 63-66. | MR | Zbl
,[11] An introduction to the Theory of Numbers, Oxford Science Publications, Fifth Edition (1979). | MR | Zbl
and ,[12] An Inequality about Irreducible Factors of Integer Polynomials, J. Number Theory 30 (1988), 156-166. | MR | Zbl
,