Regular triangular forms of rank exceeding 3

Mingyu Kim

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arXiv · 2209.13238

Regular triangular forms of rank exceeding 3

Mingyu Kim

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Abstract

A triangular form is defined to be an integer-valued quadratic polynomial of the form $a_1P_3(x_1)+a_2P_3(x_2)+\cdots+a_kP_3(x_k)$ where $a_i's$ are positive integers and $P_3(x)=x(x+1)/2$. A triangular form is called regular if it represents all positive integers which are locally represented. In this article, we find all regular triangular forms of more than three variables.

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Mingyu Kim. 2022-09-27. Regular triangular forms of rank exceeding 3. https://arxiv.org/abs/2209.13238

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