Evaluation of the convolution sums ∑l+36m=n σ(l)σ(m) and ∑4l+9m=n σ(l)σ(m)

DOI10.1142/S1793042115500104zbMath1390.11016MaRDI QIDQ2941077

Dongxi Ye

Publication date: 21 January 2015

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

zbMATH Keywords

convolution sumsrepresentation by quadratic 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) Dedekind eta function, Dedekind sums (11F20) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (14)

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 \(ab\leq 9\) ⋮ Evaluation of the convolution sums ∑a1m1+a2m2+a3m3+a4m4=nσ(m1)σ(m2)σ(m3)σ(m4) with lcm(a1,a2,a3,a4) ≤ 4 ⋮ 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) ⋮ Convolution sums of a divisor function for prime levels ⋮ 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

• 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
• 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
• Nineteen quaternary quadratic forms
• 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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