T2. 5. Estimates for ζ and PNT

Question 1

Define the analytic continuation of ζ and how we find it

Answer 1

ζ(s) has analytic continuation at R(s) > 0 apart from a simple pole at s = 1, by partial summation.

Question 2

Define the analytic continuation of ζ and how we find it

Answer 2

ζ(s) has analytic continuation at R(s) > 0 apart from a simple pole at s = 1, by partial summation.