I need your help/ How can I say this in exact math terms: Assume zeta (s)-zeta(1-s)=0. Therefore because zeta (s)-zeta(1-s) =0 the Sum 1/n^s - Sum 1/n^(1-s) or sum(( 1/n^s) -1/n^(1-s) ) converge to zero in the critical strip. I want to use the identity theorem or Uniqueness of the analytic continuation. Please help
Sir, Is it not Uniqueness theorm ? (Uniqueness Theorem) Suppose f(z) is analytic in a do- main D, and that {zn} is a sequence of distinct points converging to a point z0 in D. If f(zn)=0 for each n, then f(z) ≡ 0 throughout D.
![Complex Analysis 30 | Identity Theorem [dark version]](/img/n.gif)
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Another question set {1/n I n € N} has an accumulation point at zero. Is this correct?
Yes, that's right.
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I need your help/ How can I say this in exact math terms: Assume zeta (s)-zeta(1-s)=0. Therefore because zeta (s)-zeta(1-s) =0 the Sum 1/n^s - Sum 1/n^(1-s) or sum(( 1/n^s) -1/n^(1-s) ) converge to zero in the critical strip.
I want to use the identity theorem or Uniqueness of the analytic continuation. Please help
Sorry, I don't have the time to sit down and work this out right now.
Sir, Is it not Uniqueness theorm ?
(Uniqueness Theorem) Suppose f(z) is analytic in a do-
main D, and that {zn} is a sequence of distinct points converging to a point
z0 in D. If f(zn)=0 for each n, then f(z) ≡ 0 throughout D.
Yes, this is also known as the identity theorem
found