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)

DOI10.1142/S1793042114500341zbMath1318.11002MaRDI QIDQ3190776

Dongxi Ye, Shaun Cooper

Publication date: 19 September 2014

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

modular formsconvolution sumssum of squaresquasimodular forms

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Arithmetic functions; related numbers; inversion formulas (11A25)

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Cites Work

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• 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
• Zeta-functions of elliptic curves of 2-power conductor
• Elliptic Modular Forms and Their Applications
• 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 $\sum\limits_{m<n/9}\sigma(m)\sigma(n-9m)$

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