A modified CFKRS recipe correctly predicts the secondary main term in the second moment of Dirichlet L-functions along cosets by incorporating the non-independence of root numbers and coefficients.
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Remarks on the distribution of Dirichlet $L$-functions along cosets
A modified CFKRS recipe correctly predicts the secondary main term in the second moment of Dirichlet L-functions along cosets by incorporating the non-independence of root numbers and coefficients.