The eighth moment of Dirichlet L-functions |
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| Authors: | Vorrapan Chandee Xiannan Li |
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| Institution: | 1. Department of Mathematics, Burapha University, 169 Long-Hard Bangsaen Road, Saensook Municipality, Muang District, Chonburi, 20131, Thailand;2. University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK |
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| Abstract: | We prove an asymptotic for the eighth moment of Dirichlet L-functions averaged over primitive characters χ modulo q , over all moduli q?Q and with a short average on the critical line, conditionally on GRH. We derive the analogous result for the fourth moment of Dirichlet twists of GL(2)L-functions. Our results match the moment conjectures in the literature; in particular, the constant 24 024 appears as a factor in the leading order term of the eighth moment. |
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| Keywords: | primary 11M06 secondary 11M26 |
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