Some relations between t(a,b,c,d;n) and N(a,b,c,d;n)

Zhi-Hong Sun

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arXiv · 1511.06177

Some relations between t(a,b,c,d;n) and N(a,b,c,d;n)

Zhi-Hong Sun

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Abstract

Let $\Bbb Z$ and $\Bbb N$ be the set of integers and the set of positive integers, respectively. For $a,b,c,d,n\in\Bbb N$ let $N(a,b,c,d;n)$ be the number of representations of $n$ by $ax^2+by^2+cz^2+dw^2$, and let $t(a,b,c,d;n)$ be the number of representations of $n$ by $ax(x-1)/2+by(y-1)/2+cz(z-1)/2 +dw(w-1)/2$ $(x,y,z,w\in\Bbb Z$). In this paper we reveal some connections between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$.

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Zhi-Hong Sun. 2015-12-07. Some relations between t(a,b,c,d;n) and N(a,b,c,d;n). https://arxiv.org/abs/1511.06177

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