Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m)

DOI10.1142/S1793042116500019zbMath1360.11010OpenAlexW2120535745MaRDI QIDQ5743841

Yavuz Kesicioğlu, Şaban Alaca

Publication date: 8 February 2016

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

Full work available at URL: https://doi.org/10.1142/s1793042116500019

zbMATH Keywords

Eisenstein seriesrepresentationsmodular formscusp formsDedekind eta functionconvolution sumssum of divisors functionoctonary quadratic formsEisenstein 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) Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (13)

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 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 ⋮ Unnamed Item ⋮ Evaluation of the convolution sum \(\sum_{Al+bm=n} \sigma(l) \sigma(m)\) for \((a,b)=(1,48),(3,16),(1,54),(2,27)\) ⋮ Evaluation of convolution sums \(\sum_{l+15m=n} \sigma (l) \sigma (m)\) and \(\sum_{3l+5m=n} \sigma (l) \sigma (m)\)

Cites Work

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• Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\)
• The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\)
• The number of representations of a positive integer by certain octonary quadratic forms
• 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)
• THE REPRESENTATION NUMBERS OF THREE OCTONARY QUADRATIC FORMS
• EVALUATION OF THE CONVOLUTION SUMS ∑_l+15m=nσ(l)σ(m) AND ∑_3l+5m=nσ(l)σ(m) AND AN APPLICATION
• FOURTEEN OCTONARY QUADRATIC FORMS
• The Convolution Sum Σ_m<n/16σ(m)σ(n – 16m)
• THE CONVOLUTION SUM $\sum\limits_{m<n/9}\sigma(m)\sigma(n-9m)$

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