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Post Closed as "Not suitable for this site" by Emil Jeřábek, Francois Ziegler, David Handelman, user44191, Alex M.
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user64494
user64494
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Let us consider $$f(z):=\sum\limits_{j=1}^{j=n}a_j\sin(\lambda_jz) $$ where all $a_j$ and $\lambda_j$ (of course, $\lambda_j$ are distinct) are real numbers and $n \in \mathbb{Z},\, n \ge 2$ $n \in \mathbb{Z},\, n \ge 3$. The question is: are all the zeroes of $f(z)$ real?

Let us consider $$f(z):=\sum\limits_{j=1}^{j=n}a_j\sin(\lambda_jz) $$ where all $a_j$ and $\lambda_j$ (of course, $\lambda_j$ are distinct) are real numbers and $n \in \mathbb{Z},\, n \ge 2$ . The question is: are all the zeroes of $f(z)$ real?

Let us consider $$f(z):=\sum\limits_{j=1}^{j=n}a_j\sin(\lambda_jz) $$ where all $a_j$ and $\lambda_j$ (of course, $\lambda_j$ are distinct) are real numbers and $n \in \mathbb{Z},\, n \ge 3$. The question is: are all the zeroes of $f(z)$ real?

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user64494
user64494
  • 3.5k
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  • 22

Zeroes of linear combination of sines

Let us consider $$f(z):=\sum\limits_{j=1}^{j=n}a_j\sin(\lambda_jz) $$ where all $a_j$ and $\lambda_j$ (of course, $\lambda_j$ are distinct) are real numbers and $n \in \mathbb{Z},\, n \ge 2$ . The question is: are all the zeroes of $f(z)$ real?