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{c}

If $f$ and $g$ have respective weights $k$ and $l$, and $r=k-l>2$, unfolding the weight-$r$ Eisenstein series gives
$$
\langle f,gG_r\rangle
=\frac{2\zeta(r)\Gamma(k-1)}{(4\pi)^{k-1}}L(f,g,k-1).
$$


Rankin–Selberg unfolding identity for a holomorphic Eisenstein series

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 137 / 2 / d / Solution

Rankin–Selberg unfolding identity for a holomorphic Eisenstein series

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Rankin–Selberg unfolding identity for a holomorphic Eisenstein series

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