Zeros of Dedekind zeta functions under GRH (Q2792374)

Let \(K\) be an algebraic number field of degree \(n\) and discriminant \(d\), and for \(a\in (0,2)\) denote by \(N_K(T;a)\) the number of non-trivial zeros \(\rho\) of \(\zeta_K(s)\) satisfying \(\Im\rho\in[T-a,T+a]\). The authors show that under the General Riemann Hypothesis one has NEWLINE\[NEWLINEN_K(T;a)\leq{a\over2}f_K(1/2+a/4+iT),NEWLINE\]NEWLINE where \(f_K(z)\) is defined for \(z=\sigma+it\) by NEWLINE\[NEWLINEf_K(z)=Q+2\left({n\over1-\sigma}-{\log(2\sigma-1)\over\pi}+{0.64\over2\sigma-1}+1.37\right)Q^{2(1-\sigma)}+n\left({0.14\over2\sigma-1}-20\right),NEWLINE\]NEWLINE with \(Q=\log|d|+(\log T+20)n+11\).