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it can be shown that this field is:formula_86so that all such functions are rational functions in the weierstrass function and its derivative.
it can be shown that this field is:formula_95so that all such functions are rational functions in the weierstrass function and its derivative.

definimos:formula_2como la seri de dirichlet de la variable compleja "s", que es el producto infinito de las funciones zeta local:formula_3then formula_4, according to our definition, is well-defined only up to multiplication by rational functions in a finite number of formula_5.
we define:formula_1to be the dirichlet series of the complex variable "s", which is the infinite product of the local zeta functions:formula_2then "z"("s"), according to our definition, is well-defined only up to multiplication by rational functions in a finite number of formula_3.