Higher logarithmic-derivative moments at s=1 over Dirichlet characters of prime modulus converge to an explicit series, but the advertised exceptional-zero application is missing from the body.
Heath-Brown,Fractional moments of DirichletL-functions, Acta Arith., 145(4), 397–409, 2010
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Moments of Higher Logarithmic Derivatives and Exceptional Zeros in Cyclotomic Fields
Higher logarithmic-derivative moments at s=1 over Dirichlet characters of prime modulus converge to an explicit series, but the advertised exceptional-zero application is missing from the body.