{"docId":106,"paperId":106,"url":"https:\/\/hrj.episciences.org\/106","doi":"10.46298\/hrj.1984.106","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":18,"name":"Volume 7 - 1984"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01104327","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01104327v1","dateSubmitted":"2015-03-03 16:13:41","dateAccepted":"2015-06-12 16:05:22","datePublished":"1984-01-01 08:00:00","titles":{"en":"On the algebraic differential equations satisfied by some elliptic function I\r\n"},"authors":["Chowla, P","Chowla, S"],"abstracts":{"en":"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."},"keywords":[{"en":"algebraic differential equation"},"[MATH] Mathematics [math]"]}