Z Function - Behavior of The Z-function

Behavior of The Z-function

From the critical line theorem, it follows that the density of the real zeros of the Z-function is

for some constant c > 2/5. Hence, the number of zeros in an interval of a given size slowly increases. If the Riemann hypothesis is true, all of the zeros in the critical strip are real zeros, and the constant c is one. It is also postulated that all of these zeros are simple zeros.