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On a generalization of Waring's conjecture Zou, Chenglong

Abstract

Pupyrev's paper "Effectivization of a Lower Bound for; (4/3)^k; " provides partial results to the assertion that the distance from (4/3)^k to the nearest integer is at least (4/9)^k when k is at least 6. This is equivalent to a generalization of Waring's conjecture, which asks about the representation of integers as the sum of powers. In this writeup, we follow his work in order to complete his results. Part of the work depends on three constants, alpha, beta and gamma, which can be chosen almost without restriction, so we develop an algorithm that determines the best choice of constants for our purposes.

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