P Chowla ; S Chowla - On the algebraic differential equations satisfied by some elliptic function I

hrj:106 - Hardy-Ramanujan Journal, January 1, 1984, Volume 7 - 1984 - https://doi.org/10.46298/hrj.1984.106
On the algebraic differential equations satisfied by some elliptic function IArticle

Authors: P Chowla 1; S Chowla 2

When a is an odd positive integer it is implicit in the work of Jacobi that the functions Y=1σa(n)Xn where σa(n)=d/nda (the sum of the ath 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,Y1,,Ym)=0. When a=1 we give a new argument based on Ramanujan that we may take m=3 here.


Volume: Volume 7 - 1984
Published on: January 1, 1984
Imported on: March 3, 2015
Keywords: algebraic differential equation,[MATH]Mathematics [math]

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