On the zeros of the zeta-function
We recall from Section 2.8 that the Riemann zeta-function is defined for any complex number s = σ + it with σ > 1 by the equation
The series converges in the region of definition and indeed uniformly for σ > 1 + δ with δ > 0. The function can be continued analytically to the region σ > −1 by the equation
where f (x) is the ‘saw-tooth’ function given by
f (x) = [x] − x +
and xs+1 = exp((s + 1) ...