An Integral Equation for Riemann’s Zeta Function and Its Approximate Solution

Figure 6

For several values of σ and t, this is a comparison of and as they exist (left) and as they are predicted to exist by the approximation (right) (see (118)). In both cases, the functions have been scaled by a factor . (a) A comparison of for two very different values of σ near t = 700. (b) A comparison of the left- and right-hand sides of (118) for two very different values of σ near t = 500.

(a)

(b)