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Does there exist a (meromorphic) elementary function $f(z)$ that is zero at all the positive integers $z = 1, 2, 3, \ldots$ and only at those points? (I apologize if this problem is trivial.) Edit: an elementary function can be written as a finite composition of constants, rational functions, exponentials and logarithms. Obviously a function with those zeros can be constructed using the gamma function or a Weierstrass product, but the question is whether there is an elementary function. |
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Elementary functions with zeros only at the positive integersDoes there exist a (meromorphic) elementary function $f(z)$ that is zero at all the positive integers $z = 1, 2, 3, \ldots$ and only at those points? (I apologize if this problem is trivial.) Edit: an elementary function can be written as a finite composition of constants, rational functions, exponentials and logarithms. |
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Elementary functions with zeros only at the positive integersDoes there exist a (meromorphic) elementary function $f(z)$ that is zero at all the positive integers $z = 1, 2, 3, \ldots$ and only at those points? (I apologize if this problem is trivial.)
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