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Ramanujan's theta functions and linear combinations of four triangular numbers | | Zhi-Hong Sun
; | | Date: |
27 Nov 2018 | | Abstract: | Let $Bbb Z$ and $Bbb N$ be the set of integers and the set of positive
integers, respectively. For $a,b,c,d,ninBbb N$ 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
$ $(x,y,z,winBbb Z)$. In this paper, by using Ramanujan’s theta functions
$varphi(q)$ and $psi(q)$ we present some formulas and conjectures on
$t(a,b,c,d;n)$. | | Source: | arXiv, 1812.1109 | | Services: | Forum | Review | PDF | Favorites | |
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