Evaluation of convolution sums \(\sum_{l+15m=n} \sigma (l) \sigma (m)\) and \(\sum_{3l+5m=n} \sigma (l) \sigma (m)\)

DOI10.1007/s13226-022-00222-zzbMath1501.11014OpenAlexW4210777386MaRDI QIDQ2095092

K. R. Vasuki, Pushpa

Publication date: 9 November 2022

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-022-00222-z

zbMATH Keywords

Eisenstein seriesDedekind eta functionRamanujan's theta functiondivisors 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) Dedekind eta function, Dedekind sums (11F20) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Arithmetic functions; related numbers; inversion formulas (11A25)

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• Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
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• Evaluation of the convolution sums ∑_l+36m=n σ(l)σ(m) and ∑_4l+9m=n σ(l)σ(m)
• Ramanujan's Theta Functions
• 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
• On the number of representations of certain quadratic forms in 8 variables
• 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)