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Article Dans Une Revue Hardy-Ramanujan Journal Année : 1984

On the algebraic differential equations satisfied by some elliptic function I

Résumé

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.
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Dates et versions

hal-01104327 , version 1 (16-01-2015)

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Citer

P Chowla, S Chowla. On the algebraic differential equations satisfied by some elliptic function I . Hardy-Ramanujan Journal, 1984, Volume 7 - 1984, pp.11-12. ⟨10.46298/hrj.1984.106⟩. ⟨hal-01104327⟩
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