Geodesic
Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$
Zhi-Hong Sun1
1 School of Mathematical Sciences Huaiyin Normal University Huaian, Jiangsu 223001, P.R. China <a href="http://www.hytc.edu.cn/xsjl/szh">http://www.hytc.edu.cn/xsjl/szh</a>
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 269-289.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For given positive integers $a,b,c,d$ and $n$ let $N(a,b,c,d;n)$ be the number of representations of $n$ as $ax^2+by^2+cz^2+dw^2$, and let $t(a,b,c,d;n)$ be the number of representations of $n$ as $ax(x-1)/2+by(y-1)/2+cz(z-1)/2 +dw(w-1)/2$ $(x,y,z,w\in\Bbb Z$). By using Ramanujan’s theta functions we reveal some connections between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$.
DOI : 10.4064/aa8418-5-2016
Keywords: given positive integers d c number representations c number representations x y z w w bbb using ramanujan theta functions reveal connections between c c

Zhi-Hong Sun 1

1 School of Mathematical Sciences Huaiyin Normal University Huaian, Jiangsu 223001, P.R. China <a href="http://www.hytc.edu.cn/xsjl/szh">http://www.hytc.edu.cn/xsjl/szh</a> 
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     title = {Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$},
     journal = {Acta Arithmetica},
     pages = {269--289},
     publisher = {mathdoc},
     volume = {175},
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     year = {2016},
     doi = {10.4064/aa8418-5-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8418-5-2016/}
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Zhi-Hong Sun. Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 269-289. doi : 10.4064/aa8418-5-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8418-5-2016/

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