Skip to content
Research Article Open access CC BY 3.0

The Convolution Sum ∑m

Aeran Kim

Journal of Advances in Mathematics and Computer Science · pp. 774–789 · Published 18 Dec 2013

10.9734/BJMCS/2014/7519

Abstract

The convolution sum  m<n=8 _3(m)_3(n - 8m) is evaluated for all n 2 N. This evaluation is used to determine the formulae of the convolution sums   etc., and the number of representations of n through the sum of eight triangular numbers. 

Divisor functions : Convolution sum.

References (6)

  1. 1 Modular Forms, a Computational Approach [DOI]
  2. 2 Modular Forms - A Classical and Computational Introduction [DOI]
  3. 3 EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS [DOI]
  4. 4 Powers of theta functions [DOI]
  5. 5 Quintic and septic Eisenstein series [DOI]
  6. 6 Evaluation of two convolution sums involving the sum of divisors function [DOI]

Cited by 7

Eisenstein series and convolution sums

Zafer Selçuk Aygin · The Ramanujan journal · 2016

Article metrics

Real usage data collected on this platform.

66

Page views

0

PDF downloads

11

Outbound clicks

7

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.