On the zeros of the zeta function of one ternary quadratic form
In this paper the author reports on his calculations about the zeros of the Epstein zeta function corresponding to sums of three squares. It suffices to consider zeros with nonnegative imaginary part. The computations carried by the author demonstrate that among all the roots with imaginary part not exceeding 160000, there are exactly 95794 of them whose real part is \(3/4\) and exactly 202634 of them whose real part is bigger than \(3/4\). In general, if \(C(T)\) is the number of such zeros with real part \(3/4\) and imaginary part not exceeding \(T\), then the computations of the author suggest that the ratio \(C(T)/T\) stabilizes near 0.6 as \(T\) increases. The author gives some heuristics on the distribution of zeros as well.
scientific article; zbMATH DE number 6111013