Abstract
We provide two new proofs of the identity {fx253-1} where °(n)=d 1(n)−d 2(n) andd i (n) is the number of divisors ofn congruent toi mod 3. Furthermore, we express the number of solutions of the Diophantine equationx 2+3y 2=N in terms of δ(N).
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Farkas, H.M., Godin, Y. Logarithmic derivatives of theta functions. Isr. J. Math. 148, 253–265 (2005). https://doi.org/10.1007/BF02775438
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DOI: https://doi.org/10.1007/BF02775438