Evaluation of the convolution sums ∑a1m1+a2m2+a3m3+a4m4=nσ(m1)σ(m2)σ(m3)σ(m4) with lcm(a1,a2,a3,a4) ≤ 4

DOI10.1142/S1793042117501160zbMath1411.11007OpenAlexW2594599357MaRDI QIDQ5357497

Joohee Lee, Yoon Kyung Park

Publication date: 8 September 2017

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

Full work available at URL: https://doi.org/10.1142/s1793042117501160

zbMATH Keywords

convolution sumquasimodular formsums of divisor functionsnumber 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)

Related Items (1)

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Cites Work

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