On Polynomial Representation Functions for Multilinear Forms
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چکیده
Given an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1+ · · ·+ak, a1, . . . , ak ∈ A, is not constant for n large enough. This result is a corollary of our main theorem, which partially answers a question of Sárközy and Sós on representation functions for multilinear forms. The main tool used in the argument is an application of the Transfer Theorem for asymptotic enumeration by Flajolet and Odlyzko.
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تاریخ انتشار 2011