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The Amplitwist
The Amplitwist
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Nevanlinna's theoremNevanlinna's theorem:

Suppose $f(z)$ and $g(z)$ are two functions meromorphic in the plane. Suppose also that there are five distinct numbers $a_1,\ldots,a_5$ such that the solution sets $\lbrace z : f(z) = a_i\rbrace$ and $\lbrace z : g(z) = a_i\rbrace$ are equal. Then either $f(z)$ and $g(z)$ are equal everywhere or they are both constant.

Nevanlinna's theorem:

Suppose $f(z)$ and $g(z)$ are two functions meromorphic in the plane. Suppose also that there are five distinct numbers $a_1,\ldots,a_5$ such that the solution sets $\lbrace z : f(z) = a_i\rbrace$ and $\lbrace z : g(z) = a_i\rbrace$ are equal. Then either $f(z)$ and $g(z)$ are equal everywhere or they are both constant.

Nevanlinna's theorem:

Suppose $f(z)$ and $g(z)$ are two functions meromorphic in the plane. Suppose also that there are five distinct numbers $a_1,\ldots,a_5$ such that the solution sets $\lbrace z : f(z) = a_i\rbrace$ and $\lbrace z : g(z) = a_i\rbrace$ are equal. Then either $f(z)$ and $g(z)$ are equal everywhere or they are both constant.

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Guntram
Guntram
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Nevanlinna's theorem:

Suppose f(z)$f(z)$ and g(z)$g(z)$ are two functions meromorphic in the plane. Suppose also that there are five distinct numbers a_1, ..., a_5$a_1,\ldots,a_5$ such that the solution sets {z : f(z) = a_i}$\lbrace z : f(z) = a_i\rbrace$ and {z : g(z) = a_i}$\lbrace z : g(z) = a_i\rbrace$ are equal. Then either f(z)$f(z)$ and g(z)$g(z)$ are equal everywhere or they are both constant.

Nevanlinna's theorem:

Suppose f(z) and g(z) are two functions meromorphic in the plane. Suppose also that there are five distinct numbers a_1, ..., a_5 such that the solution sets {z : f(z) = a_i} and {z : g(z) = a_i} are equal. Then either f(z) and g(z) are equal everywhere or they are both constant.

Nevanlinna's theorem:

Suppose $f(z)$ and $g(z)$ are two functions meromorphic in the plane. Suppose also that there are five distinct numbers $a_1,\ldots,a_5$ such that the solution sets $\lbrace z : f(z) = a_i\rbrace$ and $\lbrace z : g(z) = a_i\rbrace$ are equal. Then either $f(z)$ and $g(z)$ are equal everywhere or they are both constant.

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John D. Cook
John D. Cook
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Nevanlinna's theorem:

Suppose f(z) and g(z) are two functions meromorphic in the plane. Suppose also that there are five distinct numbers a_1, ..., a_5 such that the solution sets {z : f(z) = a_i} and {z : g(z) = a_i} are equal. Then either f(z) and g(z) are equal everywhere or they are both constant.