Work

On the Order of Four-Dimensional Regular Polytope Numbers

Year: 2025

Type: article

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 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 .

Source: Results in Mathematics

DOI: 10.1007/s00025-025-02498-z

Authors: Anji Dong, The Nguyen, Alexandru Zaharescu

Institutions: University of Illinois Urbana-Champaign, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W7080717287