Short second moment bound for GL(2) L-functions in q-aspect

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2025年5月23日

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Agniva Dasgupta

摘要

We prove a Lindelöf-on-average upper bound for the second moment of the L-functions associated to a level 1 holomorphic cusp form, twisted along a coset of subgroup of the characters modulo $q^{2/3}$ $q^{2 / 3}$ (where $q = p^3$ $q = p^{3}$ for some odd prime p). This result should be seen as a q-aspect analogue of Anton Good’s (Mathematika 29(2):278–295, 1982) result on upper bounds of the second moment of cusp forms in short intervals. The results generalize easily to higher prime powers as well.