Evaluation of the convolution sums \(\Sigma_{al+bm=n}\,l \sigma(l)\sigma(m)\) with \(ab\leq 9\)

DOI10.1515/math-2017-0116zbMath1430.11007OpenAlexW2772587306MaRDI QIDQ1687059

Yoon Kyung Park

Publication date: 19 December 2017

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/math-2017-0116

zbMATH Keywords

divisor functionconvolution sumquasimodular form

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Arithmetic functions; related numbers; inversion formulas (11A25)

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• Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
• Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\)
• Powers of theta functions
• The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\)
• Quintic and septic Eisenstein series
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• Evaluation of the convolution sums ∑_l+20m=n σ(l)σ(m), ∑_4l+5m=n σ(l)σ(m) and ∑_2l+5m=n σ(l)σ(m)
• Evaluation of the convolution sum ∑_i+25j=n σ(i)σ(j)
• EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS
• Evaluation of the convolution sums \sum_{l+18m=n} \sigma(l) \sigma(m) and \sum_{2l+9m=n} \sigma(l) \sigma(m)
• EVALUATION OF THE CONVOLUTION SUMS ∑_l+15m=nσ(l)σ(m) AND ∑_3l+5m=nσ(l)σ(m) AND AN APPLICATION
• The Convolution Sum Σ_m<n/16σ(m)σ(n – 16m)
• Evaluation of two convolution sums involving the sum of divisors function
• THE CONVOLUTION SUM $\sum\limits_{m<n/9}\sigma(m)\sigma(n-9m)$
• Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m)