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We prove an exact formula for the second moment of Rankin–Selberg
is a fixed holomorphic cusp form and
is summed over automorphic forms of a given level
. The formula is a reciprocity relation that exchanges the twist parameter
and the level
. The method involves the Bruggeman–Kuznetsov trace formula on both ends; finally the reciprocity relation is established by an identity of sums of Kloosterman sums.
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