Logarithmic derivatives of theta functions

Hershel M. Farkas*, Yves Godin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We provide two new proofs of the identity ∑n=0 δ(3n + 1)xn = ∏n=1∞ (1-x3n)3/(1-xn) where δ(n) = d 1(n) - d2(n) and di(n) is the number of divisors of n congruent to i mod 3. Furthermore, we express the number of solutions of the Diophantine equation x2 + 3y2 = N in terms of δ(N).

Original languageAmerican English
Pages (from-to)253-265
Number of pages13
JournalIsrael Journal of Mathematics
StatePublished - 2005


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