DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES

We consider Weierstrass functions and divisor functions arising from q-series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any n ≥ 1, we have [Formula Presented] Finally, we shall give a table for E₁ (N; 3), σ(N), τ_1;3,1 (N) and τ_2;3,1 (N) (1 ≤ N ≤ 50) and state simulation results for them.