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On the expressibility of a uniform function of several complex variables as the quotient of two functions of entire character

On the expressibility of a uniform function of several complex variables as the quotient of two functions of entire character

In the theory of Theta functions, this condition expresses the fact that the period system •rn, Ti2, 1-22 is non-singular.f This has the advantage of simplifying the convergence proof for the series (19).* The following investigation is closely related to one made by Appell to an entirely different purpose in …