Zeros of Derivatives

The Observer · **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?

Thanks in advance!!

Shadow · **Posted:** Thu, 31 May 2012 04:03:42 UTC

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?

Thanks in advance!!

That's not true, take $f(z)=z\sin z$ and consider the zero at z=0

.

The Observer · **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.

Shadow · **Posted:** Thu, 31 May 2012 16:52:48 UTC

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.

Shadow · **Posted:** Thu, 31 May 2012 16:52:56 UTC

Topic moved to analysis.

S.O.S. Mathematics CyberBoard

Zeros of Derivatives

Who is online