On the order of 4-dimensional regular polytope numbers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909433108365312 |
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| author | Dong, Anji Nguyen, The Zaharescu, Alexandru |
| author_facet | Dong, Anji Nguyen, The Zaharescu, Alexandru |
| contents | 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 $f(1)=1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the order of 4-dimensional regular polytope numbers Dong, Anji Nguyen, The Zaharescu, Alexandru Number Theory Combinatorics 11P05, 11P55, 11L07, 11L15, 05A16 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 $f(1)=1$. |
| title | On the order of 4-dimensional regular polytope numbers |
| topic | Number Theory Combinatorics 11P05, 11P55, 11L07, 11L15, 05A16 |
| url | https://arxiv.org/abs/2412.13974 |