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We investigate the distribution of large positive (and negative) values of the Euler–Kronecker constant γ Q ( D ) of the quadratic field Q ( D ) as D varies over fundamental discriminants | D | ≤ x . We show that the distribution function of these values is very well approximated by that of an adequate probabilistic random model in a large uniform range. The main tools are an asymptotic formula for the Laplace transform of γ Q ( D ) together with a careful saddle point analysis. [ABSTRACT FROM AUTHOR]

J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We find analogous expressions for the product of two Dedekind zeta functions and then use these expressions to find some expressions for Dedekind zeta values attached to arbitrary real as well as quadratic number fields at any positive integer. [ABSTRACT FROM AUTHOR]

Let L be an automorphic L -function. Assuming the Riemann Hypothesis for L (s) and the Selberg normality conjecture, we obtain a lower bound for the second negative moment and extreme small values of L ′ (ρ) , where ρ is a zero of L (s). [ABSTRACT FROM AUTHOR]