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We give a number field analogue of a result of Ramanujan, Hardy andLittlewood, thereby obtaining a modular relation involving the non-trivialzeros of the Dedekind zeta function. We also provide a Riesz-type criterion forthe Generalized Riemann Hypothesis for $\zeta_K(s)$. New eleganttransformations are obtained when $K$ is a quadratic extension, one of whichinvolves the modified Bessel function of the second kind.

A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis