On the Order of Four-Dimensional Regular Polytope Numbers

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2025年8月14日

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Anji Dong,
The Nguyen,
Alexandru Zaharescu

摘要

In light of Kim’s conjecture on regular polytopes of dimension four, which is a generalization of Waring’s problem, we establish asymptotic formulas for representing any sufficiently large integer as a sum of numbers in the form of those regular 4-polytopes. Moreover, we obtain a more general result of the asymptotics for any degree-four polynomial f satisfying $f(0)=0$ $f (0) = 0$ and $f(1)=1$ $f (1) = 1$ .