The average twelfth power of Dirichlet L-function central values for odd prime power moduli q=p^n is at most p^A q^{2+ε}, the expected order up to q^ε.
Mean-Value Theorems in the Theory of the Riemann Zeta-Function
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Twelfth moment of Dirichlet L-functions to prime power moduli
The average twelfth power of Dirichlet L-function central values for odd prime power moduli q=p^n is at most p^A q^{2+ε}, the expected order up to q^ε.