Evaluation of certain convolution sums involving the sum of the divisors function

被引：0

作者：

Kokluce, Bulent ^{[1
]}

机构：

[1] Brown Univ, Inst Computat & Expt Res Math, 121 S Main St, Providence, RI 02903 USA

来源：

RAMANUJAN JOURNAL | 2023年 / 60卷 / 02期

关键词：

Sum of divisor function; Convolution sum; Eta quotients; Modular forms; Quadratic forms; Representation number; SIGMA(L)SIGMA(M);

D O I：

10.1007/s11139-022-00632-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We evaluate the convolution sums Sigma(rl+sm=n) sigma(l)sigma(m), for (r, s) = (1, 17), (1, 34), (2, 17), (1, 68) and (4, 17), for all positive integers n. We then use these evaluations to determine formula for the number of representation of a positive integer n by the octonary quadratic form x(1)(2)+x(2)(2)+x(3)(2)+x(4)(2)+17(x(5)(2)+x(6)(2)+x(7)(2)+x(8)(2)).

引用

页码：533 / 549

页数：17

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