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  1. Abstract There has recently been some interest in optimizing the error term in the asymptotic for the fourth moment of DirichletL‐functions and a closely related mixed moment ofL‐functions involving automorphicL‐functions twisted by Dirichlet characters. We obtain an improvement for the error term of the latter. 
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  2. We prove hybrid subconvexity bounds for twisted L L -functions L ( s , f × χ ) L(s,f\times \chi ) at the central point using a fourth moment estimate, including a new instance of the Burgess subconvexity bound. 
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  3. null (Ed.)
    Abstract We prove hybrid subconvexity bounds for a wide class of twisted L-functions L(s, f × χ) at the central point, including a new instance of the Weyl subconvexity bound. 
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