Evaluation of the convolution sums \(\sum_{ak+bl+cm}=\sigma(k)\sigma(l)\sigma(m)\) with \(\text{lcm}(a,b,c) \leq 6\)

DOI10.1016/j.jnt.2016.04.025zbMath1396.11006OpenAlexW2413767384MaRDI QIDQ301439

Yoon Kyung Park

Publication date: 30 June 2016

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.04.025

zbMATH Keywords

convolution sumquasimodular formthe number of representation by quadratic forms

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) 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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• Some arithmetic identities involving divisor functions
• 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
• Evaluation of the convolution sums ∑_l+36m=n σ(l)σ(m) and ∑_4l+9m=n σ(l)σ(m)
• 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)
• О представлении чисел суммами квадратичных форм $x_{1}^{2} + x_{1}x_{2} + x_{2}^{2}$
• 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)
• EVALUATION OF THE CONVOLUTION SUMS ∑_i+3j=nσ(i)σ₃(j) AND ∑_3i+j=nσ(i)σ₃(j)