| 1. | The theorem follows from the fact that holomorphic functions are analytic.
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| 2. | The holomorphic functions " g " have the property that
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| 3. | Choice of P _ 0 gives rise to a standard holomorphic function
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| 4. | Which extends our original definition to a holomorphic function of t.
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| 5. | One way of depicting holomorphic functions is with a Riemann surface.
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| 6. | That is, a holomorphic function is a modular function if
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| 7. | This follows directly from the identity theorem for holomorphic functions.
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| 8. | This is used to show existence theorems for holomorphic functions.
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| 9. | This can be expressed in terms of a single holomorphic function F.
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| 10. | This is also the initial topology for the family of holomorphic functions.
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