Lecture 18

Question 1

Uniqueness theorem

Answer 1

Given two Dirichlet series

• F(s) = ∑_(n=1)^∞ f(n)/n^s
• G(s) = ∑_(n=1)^∞ g(n)/n^s

both absolutely convergent for σ > σ_a. If F(s) = G(s) for each s is an infinite sequence {sk} such that σ_k → ∞ as k → ∞, then f(n) = g(n) for all n