| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
20 April 2024 |
|
| | | |
|
Article overview
| |
|
Some relations between t(a,b,c,d;n) and N(a,b,c,d;n) | Zhi-Hong Sun
; | Date: |
19 Nov 2015 | 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 $N(a,b,c,d;n)$ 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
$ax(x-1)/2+by(y-1)/2+cz(z-1)/2
+dw(w-1)/2$ $(x,y,z,winBbb Z$). In this paper we reveal some connections
between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$. Suppose $a,ninBbb N$ and $aequiv
1pmod 2$. We show that $$t(a,b,c,d;n)=frac
23(N(a,b,c,d;8n+a+b+c+d)-N(a,b,c,d;2n+(a+b+c+d)/4))$$ for $(a,b,c,d)=
(a,a,2a,8m+4)$ and $(a,3a,4k+2,4m+2)$ with $kequiv mpmod 2$. | Source: | arXiv, 1511.6177 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |