Evaluation of the convolution sum ∑i+25j=n σ(i)σ(j)

DOI10.1142/S1793042114500365zbMath1318.11005OpenAlexW2158201382MaRDI QIDQ3190778

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Publication date: 19 September 2014

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

Full work available at URL: https://doi.org/10.1142/s1793042114500365

zbMATH Keywords

Eisenstein seriesconvolution sumssum of divisors function

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) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (16)

Evaluation of the convolution sums \(\sum_{ak+bl+cm}=\sigma(k)\sigma(l)\sigma(m)\) with \(\text{lcm}(a,b,c) \leq 6\) ⋮ Evaluation of the convolution sums ∑ak+bl+cm=nσ(k)σ(l)σ(m) with lcm(a,b,c) = 7,8 or 9 ⋮ EVALUATION OF CONVOLUTION SUMS AND FOR k = a · b = 21, 33, AND 35 ⋮ Evaluation of the convolution sums \(\Sigma_{al+bm=n}\,l \sigma(l)\sigma(m)\) with \(ab\leq 9\) ⋮ Eisenstein series and convolution sums ⋮ Evaluation of the convolution sums ∑a1m1+a2m2+a3m3+a4m4=nσ(m1)σ(m2)σ(m3)σ(m4) with lcm(a1,a2,a3,a4) ≤ 4 ⋮ A simple extension of Ramanujan-Serre derivative map and some applications ⋮ Evaluation of certain convolution sums involving the sum of the divisors function ⋮ Evaluation of some convolution sums and representation of integers by certain quadratic forms in 12 variables ⋮ Unnamed Item ⋮ Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52 ⋮ Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m) ⋮ Unnamed Item ⋮ Evaluation of the convolution sum \(\sum_{Al+bm=n} \sigma(l) \sigma(m)\) for \((a,b)=(1,48),(3,16),(1,54),(2,27)\) ⋮ Representations by certain octonary quadratic forms with coefficients 1, 2, 5 and 10 ⋮ Evaluation of convolution sums \(\sum_{l+15m=n} \sigma (l) \sigma (m)\) and \(\sum_{3l+5m=n} \sigma (l) \sigma (m)\)

Cites Work

• 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 \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\)
• Eisenstein series in Ramanujan's Lost Notebook
• 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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