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 Post subject: Zeros of DerivativesPosted: Thu, 31 May 2012 03:41:36 UTC

Joined: Thu, 31 May 2012 03:22:29 UTC
Posts: 6
Hello, I must prove that the derivative of the function f(z) does not equal zero at the zeros of f(z). f(z) is an infinite series. It is complex and has an infinite number of zeros. Does anyone know of a way to do this?

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 Post subject: Re: Zeros of DerivativesPosted: Thu, 31 May 2012 04:03:42 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
The Observer wrote:
Hello, I must prove that the derivative of the function f(z) does not equal zero at the zeros of f(z). f(z) is an infinite series. It is complex and has an infinite number of zeros. Does anyone know of a way to do this?

That's not true, take and consider the zero at .

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 Post subject: Re: Zeros of DerivativesPosted: Thu, 31 May 2012 16:13:40 UTC

Joined: Thu, 31 May 2012 03:22:29 UTC
Posts: 6
I am talking about specific functions, in this case, a dirichlet L-series. I read in a paper a while back that the derivative of certain dirichlet series will never equal zero when the series equals zero. I am just curious about this, they did not provide a proof, they just mentioned it. If anyone has a proof of this or a way of checking this, it would be useful for what I'm working on.

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 Post subject: Re: Zeros of DerivativesPosted: Thu, 31 May 2012 16:52:48 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
The Observer wrote:
I am talking about specific functions, in this case, a dirichlet L-series. I read in a paper a while back that the derivative of certain dirichlet series will never equal zero when the series equals zero. I am just curious about this, they did not provide a proof, they just mentioned it. If anyone has a proof of this or a way of checking this, it would be useful for what I'm working on.

"What I'm working on" is not generally a good motivator. If you can speak on which series you're talking about, or which paper you're referencing, or something more specific we might be able to help you.

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 Post subject: Re: Zeros of DerivativesPosted: Thu, 31 May 2012 16:52:56 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Topic moved to analysis.

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