episciences.org_106_1653280827
1653280827
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
01
1984
Volume 7  1984
On the algebraic differential equations satisfied by some elliptic function I
P
Chowla
S
Chowla
When $a$ is an odd positive integer it is implicit in the work of Jacobi that the functions $Y=\sum_1^{\infty} \sigma_a(n)X^n$ where $\sigma_a (n) = \sum_{d/n} d^a$ (the sum of the $a$th powers of the divisors of $n$) satisfy an algebraic differential equation; i.e., there is a polynomial $T$ not identically $0$, such that $T(X, Y, Y_1, \ldots, Y_m)=0$. When $a=1$ we give a new argument based on Ramanujan that we may take $m= 3$ here.
01
01
1984
106
https://hal.archivesouvertes.fr/hal01104327v1
10.46298/hrj.1984.106
https://hrj.episciences.org/106

https://hrj.episciences.org/106/pdf