10.46298/hrj.1984.106
https://hrj.episciences.org/106
Chowla, P
P
Chowla
Chowla, S
S
Chowla
On the algebraic differential equations satisfied by some elliptic function I
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.
episciences.org
algebraic differential equation
[MATH] Mathematics [math]
2015-06-12
1984-01-01
1984-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01104327v1
2804-7370
https://hrj.episciences.org/106/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 7 - 1984
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