On the algebraic differential equations satisfied by some elliptic function I
Chowla, P ; Chowla, S
HAL, hal-01104327 / Harvested from HAL
Text on HAL
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.
Publié le : 1984-07-04
Classification:  algebraic differential equation,  [MATH]Mathematics [math] 
@article{hal-01104327,
     author = {Chowla, P and Chowla, S},
     title = {On the algebraic differential equations satisfied by some elliptic function I},
     journal = {HAL},
     volume = {1984},
     number = {0},
     year = {1984},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01104327}
}

Chowla, P; Chowla, S. On the algebraic differential equations satisfied by some elliptic function I. HAL, Tome 1984 (1984) no. 0, . http://gdmltest.u-ga.fr/item/hal-01104327/