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.
Higher Euler-Kronecker Constants of Number fields
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abstract
The higher Euler-Kronecker constants of a number field $K$ are the coefficients in the Laurent series expansion of the logarithmic derivative of the Dedekind zeta function about $s=1$. These coefficients are mysterious and seem to contain a lot of arithmetic information. In this article, we study these coefficients. We prove arithmetic formulas satisfied by them and prove bounds. We generalize certain results of Ihara.
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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.