The question is: Find an entire function f such that f(k+il)=0 for all possible k, l integers. Find the most elementary solution possible.

This is a homework question from complex variable course. I don't understand this question. If given a sequence of zeros of entire function, then we can write a very general form of entire functions using weierstrass theory. So the question here is about how to construct this sequence? Could anybody explain this question for me? Really appreciate your help!

  • $\begingroup$ Have you been doing weierstrass factorization? $\endgroup$ – Seth Apr 16 '14 at 17:36
  • $\begingroup$ Yes.I think this question is about weierstrass factorization. But what is the an here? $\endgroup$ – MMM3333 Apr 16 '14 at 17:38
  • $\begingroup$ Just enumerate the $k+il$, say going around in a spiral in such a way that the $a_n$ will converge to infinity. $\endgroup$ – Seth Apr 16 '14 at 17:40
  • $\begingroup$ There is an even more elementary solution, not to say trivial ... Btw., how do you find entire functions with poles? $\endgroup$ – Hagen von Eitzen Apr 16 '14 at 17:41
  • $\begingroup$ @Seth, can you write the an=...., for me? then I can just put it in my weierstrass factorization.Thank you very much. $\endgroup$ – MMM3333 Apr 16 '14 at 17:55

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