On the Minimum Norm of Representatives of Residue Classes in Number Fields
نویسندگان
چکیده
In this paper we consider the problem of finding upperbounds on the minimum norm of representatives in residue classes in quotient O/I, where I is an integral ideal in the maximal order O of a number field K. In particular, we answer affirmatively a question of Konyagin and Shparlinski, stating that an upperbound o(N(I)) holds for most ideals I, denoting N(I) the norm of I. More precise statements are obtained, especially when I is prime. We use the method of exponential sums over multiplicative groups, exploiting essentially the new bounds obtained by the methods in [BC1] and [BC2].
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