On the order of 4-dimensional regular polytope numbers

Anji Dong; The Nguyen; Alexandru Zaharescu

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arXiv · 2412.13974

On the order of 4-dimensional regular polytope numbers

Anji Dong·The Nguyen·Alexandru Zaharescu

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Abstract

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 are able to obtain a more general result of the asymptotics for any degree-four polynomial $f$ satisfying $f(0)=0$ and $f(1)=1$.

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Anji Dong, The Nguyen, Alexandru Zaharescu. 2024-12-18. On the order of 4-dimensional regular polytope numbers. https://arxiv.org/abs/2412.13974

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