Abstract:
The paper presents several theorems on the linear and algebraic independence of the values at algebraic points of the set of $E$-functions related by algebraic equations over the field of rational functions, as well as some estimates of the absolute values of polynomials with integer coefficients in the values of such functions. The results are obtained by using the properties of ideals in the ring of polynomials of several variables formed by equations relating the above functions over the field of rational functions.
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