An explicit Tauberian theorem using twisted moment bounds instead of pointwise bounds yields square-root-saving error terms for counting C_n-extensions of Q for n = 3, 4, 8, 16, and 2p.
Functional equations with multiple gamma factors and the average order of arithmetical functions
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An Explicit Tauberian Theorem taking Averaged Inputs with an Application to Counting Abelian Number Fields
An explicit Tauberian theorem using twisted moment bounds instead of pointwise bounds yields square-root-saving error terms for counting C_n-extensions of Q for n = 3, 4, 8, 16, and 2p.