首页 | 本学科首页   官方微博 | 高级检索  
     


Sums of triangular numbers from the Frobenius determinant
Authors:Hjalmar Rosengren
Affiliation:Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden
Abstract:We show that the denominator formula for the strange series of affine superalgebras, conjectured by Kac and Wakimoto and proved by Zagier, follows from a classical determinant evaluation of Frobenius. As a limit case, we obtain exact formulas for the number of representations of an arbitrary number as a sum of 4m2/d triangles, whenever d|2m, and 4m(m+1)/d triangles, when d|2m or d|2m+2. This extends recent results of Getz and Mahlburg, Milne, and Zagier.
Keywords:primary, 11E25   secondary, 17B65
本文献已被 ScienceDirect 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