We consider continued fractions
(CF) |
Nous considérons une fraction continue
(FC) |
La conjecture de Ramanujan disant que la fraction diverge toujours, quand , restait ouverte jusqu'au présent. Nous montrons, qu'elle est fausse : pour tout il existe une suite réelle telle que la fraction converge. Nous montrons aussi, que la condition précedante de Gill, qui est suffisante pour que la fraction diverge, est celle optimale sur la vitesse de convergence des .
Accepted:
Published online:
@article{CRMATH_2005__341_7_427_0, author = {Glutsyuk, Alexey A.}, title = {On convergence of generalized continued fractions and {Ramanujan's} conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {427--432}, publisher = {Elsevier}, volume = {341}, number = {7}, year = {2005}, doi = {10.1016/j.crma.2005.08.001}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.08.001/} }
TY - JOUR AU - Glutsyuk, Alexey A. TI - On convergence of generalized continued fractions and Ramanujan's conjecture JO - Comptes Rendus. Mathématique PY - 2005 SP - 427 EP - 432 VL - 341 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.08.001/ DO - 10.1016/j.crma.2005.08.001 LA - en ID - CRMATH_2005__341_7_427_0 ER -
%0 Journal Article %A Glutsyuk, Alexey A. %T On convergence of generalized continued fractions and Ramanujan's conjecture %J Comptes Rendus. Mathématique %D 2005 %P 427-432 %V 341 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.08.001/ %R 10.1016/j.crma.2005.08.001 %G en %F CRMATH_2005__341_7_427_0
Glutsyuk, Alexey A. On convergence of generalized continued fractions and Ramanujan's conjecture. Comptes Rendus. Mathématique, Volume 341 (2005) no. 7, pp. 427-432. doi : 10.1016/j.crma.2005.08.001. http://archive.numdam.org/articles/10.1016/j.crma.2005.08.001/
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