Abstract:
The paper describes the basic properties of polynomial comparisons modulo an ideal in the ring of integers of an algebraic number field, estimates of total rational trigonometric sums from a polynomial over an algebraic field are found, estimates of sums of Dirichlet characters modulo the degree of a prime ideal in an algebraic field are obtained, estimates of multiples of total rational trigonometric sums from polynomials over an algebraic field are given.
Keywords:trigonometric sums, I. M. Vinogradov method, Hua Lo-ken method, ring of integers in an algebraic number field, complete rational trigonometric sums over an algebraic number field, Dirichlet characters in algebraic number fields, A. G. Postnikov formula for Dirichlet characters in an algebraic field.
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