Comptes Rendus
no. 11-12
Number theory
Odd values of the Rogers–Ramanujan functions

Presented by: the Editorial Board

Shi-Chao Chen1
1 Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, P. R. China
Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1081-1084.

Let g(n) and h(n) be the coefficients of the Rogers–Ramanujan identities. We obtain asymptotic formulas for the number of odd values of g(n) for odd n, and h(n) for even n, which improve Gordon's results. We also obtain lower bounds for the number of odd values of g(n) for even n, and h(n) for odd n.

Soit g(n) et h(n) les coefficients des identités de Rogers–Ramanujan. Nous obtenons des formules asymptotiques pour le nombre de valeurs impaires de g(n) lorsque n est impair et de h(n) lorsque n est pair. Ces formules améliorent un résultat de Gordon. Nous obtenons également des bornes inférieures pour le nombre de valeurs impaires de g(n) pour n pair et de h(n) pour n impair.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.10.002

Shi-Chao Chen 1

1 Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, P. R. China 
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Shi-Chao Chen. Odd values of the Rogers–Ramanujan functions. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1081-1084. doi : 10.1016/j.crma.2018.10.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.002/

[1] J. Bellaïche; B. Green; K. Soundararajan Nonzero coefficients of half-integral weight modular forms mod ℓ, Res. Math. Sci., Volume 5 (2018), p. 6

[2] A.J.F. Biagioli A proof of some identities of Ramanujan using modular forms, Glasg. Math. J., Volume 31 (1989), pp. 271-295

[3] B. Gordon (Dev. Math.), Volume vol. 23, Springer, New York (2012), pp. 83-93

[4] M.D. Hirschhorn On the 2- and 4-dissections of the Rogers–Ramanujan functions, Ramanujan J., Volume 40 (2016) no. 2, pp. 227-235

[5] K. Ono (CBMS Regional Conference Series in Mathematics) (2004), p. 17

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