Dirichlet Eta Function - Zeros

Zeros

The zeros of the eta function include all the zeros of the zeta function: the infinity of negative even integers (real equidistant simple zeros); an infinity of zeros along the critical line, none of which are known to be multiple and over 40% of which have been proven to be simple, and the hypothetical zeros in the critical strip but not on the critical line, which if they do exist must occur at the vertices of rectangles symmetrical around the x-axis and the critical line and whose multiplicity is unknown. In addition, the factor adds an infinity of complex simple zeros, located at equidistant points on the line, at where n is any nonzero integer.

Under the Riemann hypothesis, the zeros of the eta function would be located symmetrically with respect to the real axis on two parallel lines, and on the perpendicular half line formed by the negative real axis.