Nous prouvons des formules pour les fonctions génératrices des différences de rang pour les partitions où les parts impaires sont distinctes. Ces formules sont en termes de formes modulaires et de séries de Lambert généralisées.
We prove formulas for the generating functions for -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.
@article{JTNB_2009__21_2_313_0,
author = {Lovejoy, Jeremy and Osburn, Robert},
title = {$M_2$-rank differences for partitions without repeated odd parts},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {313--334},
publisher = {Universit\'e Bordeaux 1},
volume = {21},
number = {2},
year = {2009},
doi = {10.5802/jtnb.673},
mrnumber = {2541428},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.673/}
}
TY - JOUR AU - Lovejoy, Jeremy AU - Osburn, Robert TI - $M_2$-rank differences for partitions without repeated odd parts JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 313 EP - 334 VL - 21 IS - 2 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.673/ DO - 10.5802/jtnb.673 LA - en ID - JTNB_2009__21_2_313_0 ER -
%0 Journal Article %A Lovejoy, Jeremy %A Osburn, Robert %T $M_2$-rank differences for partitions without repeated odd parts %J Journal de théorie des nombres de Bordeaux %D 2009 %P 313-334 %V 21 %N 2 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.673/ %R 10.5802/jtnb.673 %G en %F JTNB_2009__21_2_313_0
Lovejoy, Jeremy; Osburn, Robert. $M_2$-rank differences for partitions without repeated odd parts. Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 313-334. doi : 10.5802/jtnb.673. http://www.numdam.org/articles/10.5802/jtnb.673/
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