Asymptotic Formula for the Coordinates of the Zeros of Sections of the Zeta Function, zeta(N)(s), Near s = 1

The sum, Σ1^Nn^-8 = ζN(s), s = σ + it, is called a section of the Riemann zeta function, ζ(s). Here an asymptotic formula, for large N, giving the location of the zeros of ζN(s) near s = 1 will be demonstrated. In particular these zeros will lie in σ < 1. Relationships between the location of the zeros of ζN(s) and the zeros of ζ(s) were discovered by Turán. The location in σ < 1 will also be demonstrated directly, without the asymptotic formula, together with results valid also when s - 1 is not small.