**14**

On the zeros of the zeta-function

**14.1 Introduction**

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 *x*^{s+1} = exp((*s* + 1) ...

Start Free Trial

No credit card required