摘要
For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we have r( f, n) = r( g, n) or r( f, n) ≠ r( g, n).Our method is to use elliptic curves and the corresponding new forms.
For two given ternary quadratic formsf(x, y, z) andg( x, y, z), letr(f, n) andr(g, n) be the numbers of representations of n represented byf( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we haver(f, n) =r(g, n) orr( f, n)≠r(g, n). Our method is to use elliptic curves and the corresponding new forms.
基金
the National Natural Science Foundation of China (Grant No. 19871917).
