We prove an exact formula for the second moment of Rankin–Selberg $L$ -functions $L(\frac{1}{2},f\times g)$ twisted by $\unicode[STIX]{x1D706}_{f}(p)$ , where $g$ is a fixed holomorphic cusp form and $f$ is… Click to show full abstract
We prove an exact formula for the second moment of Rankin–Selberg $L$ -functions $L(\frac{1}{2},f\times g)$ twisted by $\unicode[STIX]{x1D706}_{f}(p)$ , where $g$ is a fixed holomorphic cusp form and $f$ is summed over automorphic forms of a given level $q$ . The formula is a reciprocity relation that exchanges the twist parameter $p$ and the level $q$ . 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.
Journal Title: Mathematika
Year Published: 2018
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