Grommer inequalities

Let

\begin{displaymath}-\frac{\Xi'}{\Xi}(t)=s_1+s_2t+s_3t^2+\dots.\end{displaymath}

Let $M_n$ be the matrix whose $i,j$ entry is $s_{i+j}$. J. Grommer (J. Reine Angew. Math. 144 (1914), 114-165) proved that necessary and sufficient conditions for the truth of the Riemann Hypothesis are that

\begin{displaymath}\det M_n>0 \end{displaymath}

for all $n\ge 1.$

See also the paper of R. Alter [MR 36 #1399].



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