Eisenstein Series and Convolution Sums

We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $\sum_{a+p b=n}σ(a)σ(b)$, $\sum_{p_1a+p_2 b=n}σ(a)σ(b)$ and $\sum_{a+p_1 p_2 b=n}σ(a)σ(b)$ where $p, p_1, p_2$ are primes.

No reviews yet.

No comments yet.