Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899669 | Journal of Mathematical Analysis and Applications | 2018 | 18 Pages |
Abstract
Let N(a,b,c,d;n) and t(a,b,c,d;n) denote the number of representations of n as ax2+by2+cz2+dw2 and the number of representations of n as ax(x+1)2+by(y+1)2+cz(z+1)2+dw(w+1)2, respectively, where a,b,c,d are positive integers, n is a nonnegative integer and x,y,z,w are integers. Sun established many relations between N(a,b,c,d;n) and t(a,b,c,d;n) and posed 23 conjectures. Yao proved five of them by using (p,k)-parametrization of theta functions. In this paper, we confirm four conjectures of Sun by employing theta function identities.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ernest X.W. Xia, Z.X. Zhong,