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

2015/11/19 by Zhi-Hong Sun, Sun, Zhi-Hong
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11D85 #Secondary 11E25 #math.NT #msc:11D85 #msc:11E25

paper · pdf · doi:10.48550/arxiv.1511.06177

19 pages

openalex publication_date 2015/11/19 · arxiv created 2015/12/07 · arxiv updated 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈\Bbb N let N(a,b,c,d;n) be the number of representations of n by ax²+by²+cz²+dw², 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∈\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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