THE REPRESENTATION NUMBERS OF CERTAIN OCTONARY QUADRATIC FORMS

被引：3
|
作者：
Kokluce, Bulent [1 ]
机构：
[1] Fatih Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 05期
关键词：
Quadratic forms; sum of divisors functions; convolution sums; representation numbers; CONVOLUTION; SUMS;
D O I：
10.1142/S1793042113500164
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study we derive formulae for the number of representations of n by the octonary quadratic forms x(1)(2) + x(1)x(2) + x(2)(2) + 2x(3)(2) + 2x(3)x(4) + 2x(4)(2) + 2x(5)(2) + 2x(5)x(6) + 2x(6)(2) + 4x(7)(2) + 4x(7)x(8) + 4x(8)(2), x(1)(2) + x(1)x(2) + x(2)(2) + 2x(3)(2) + 2x(3)x(4) + 2x(4)(2) + 3x(5)(2) + 3x(5)x(6) + 3x(6)(2) + 6x(7)(2) + 6x(7)x(8) + 6x(8)(2), x(1)(2) + x(1)x(2) + x(2)(2) + 2x(3)(2) + 2x(3)x(4) + 2x(4)(2) + 4x(5)(2) + 4x(5)x(6) + 4x(6)(2) + 8x(7)(2) + 8x(7)x(8) + 8x(8)(2) for any n is an element of N-0.
引用
收藏
页码：1125 / 1139
页数：15
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