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Field theory for the function field of the quintic fermat curve

We study the structure of the function field K of the quintic Fermat curve F(5) in the following way: Let K m be a g-maximal rational subfield of K. Then the field extension K/K m is obtained by the projection from F(5) to a line with a center p, ∈ F(5). By using this fact, we consider the field extension K/K m from several point of view.