首页 | 本学科首页   官方微博 | 高级检索  
     


On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
Authors:Kachakhidze  N.
Abstract:
The systems of bases are constructed for the spaces of cusp forms 
$$S_k (Gamma _0 (3),chi )(k geqslant 6),S_k (Gamma _0 (7),chi )(k geqslant 3)$$
and 
$$S_k (Gamma _0 (11),chi )(k geqslant 3)$$
. Formulas are obtained for the number of representations of a positive integer by the sum of k binary quadratic forms of the kind 
$$x_1^2 + x_1 x_2 + x_2^2 (6 leqslant k leqslant 17)$$
, of the kind 
$$x_1^2 + x_1 x_2 + 2x_2^2 (3 leqslant k leqslant 11)$$
and of the kind 
$$x_1^2 + x_1 x_2 + 3x_1^2 (3 leqslant k leqslant 7)$$
.
Keywords:Representation of numbers by quadratic forms  direct sum of quadratic forms  space of cusp forms  generalized multiple theta-series
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号