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Ke Shi
Ke Shi
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I wonder whether $\sum_{k=0}^n \exp(r_k z)$ has a complex zero for any $0=r_0<r_1<r_2<\dotsb<r_n$$n\in \mathbb{Z}_n^*,0=r_0<r_1<r_2<\dotsb<r_n$. I think the answer is affirmative.

I wonder whether $\sum_{k=0}^n \exp(r_k z)$ has a complex zero for any $0=r_0<r_1<r_2<\dotsb<r_n$. I think the answer is affirmative.

I wonder whether $\sum_{k=0}^n \exp(r_k z)$ has a complex zero for any $n\in \mathbb{Z}_n^*,0=r_0<r_1<r_2<\dotsb<r_n$. I think the answer is affirmative.

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GH from MO
GH from MO
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WhetherI wonder whether $\sum_{k=0}^n \exp(r_k z)=0$$\sum_{k=0}^n \exp(r_k z)$ has onea complex zero for any $0=r_0<r_1<r_2<\dotsb<r_n$.

  I think itthe answer is trueaffirmative.

Whether $\sum_{k=0}^n \exp(r_k z)=0$ has one zero for $0=r_0<r_1<r_2<\dotsb<r_n$.

  I think it is true.

I wonder whether $\sum_{k=0}^n \exp(r_k z)$ has a complex zero for any $0=r_0<r_1<r_2<\dotsb<r_n$. I think the answer is affirmative.

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Ke Shi
Ke Shi
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Zeros of a complex function

Whether $\sum_{k=0}^n \exp(r_k z)=0$ has one zero for $0=r_0<r_1<r_2<\dotsb<r_n$.

I think it is true.