Explicit evaluation of triple convolution sums of the divisor functions (Q6540617)

scientific article; zbMATH DE number 7850236

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English	Explicit evaluation of triple convolution sums of the divisor functions	scientific article; zbMATH DE number 7850236

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instance of

scholarly article

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title

Explicit evaluation of triple convolution sums of the divisor functions (English)

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International Journal of Number Theory

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publication date

17 May 2024

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zbMATH Keywords

sum of divisor functions

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convolution sums of the divisor functions

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modular forms of integral weight

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MaRDI profile type

Publication

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cites work

The convolution sum $\sum_{al+bm=n} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (1,14), (2,7), (1,7)$

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Evaluation of the convolution sums \sum_{l+18m=n} \sigma(l) \sigma(m) and \sum_{2l+9m=n} \sigma(l) \sigma(m)

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Q5447637

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The Convolution Sum Σm<n/16σ(m)σ(n – 16m)

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

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Some arithmetic identities involving divisor functions

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Evaluation of the convolution sums $\sum _{l+6m=n}\sigma (l)\sigma (m)$ and $\sum _{2l+3m=n}\sigma (l)\sigma (m)$

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Eisenstein series and convolution sums

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Powers of theta functions

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Convolution sums of a divisor function for prime levels

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Quintic and septic Eisenstein series

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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)

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On the square of the series in which the coefficients are the sums of the divisors of the exponents.

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Q5795178

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Evaluation of two convolution sums involving the sum of divisors function

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О представлении чисел суммами квадратичных форм $x_{1}^{2} + x_{1}x_{2} + x_{2}^{2}$

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Q5384185

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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 Convolution Sums entailing mixed Divisor Functions for a Class of Levels

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

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Evaluation of the convolution sums ∑ak+bl+cm=nσ(k)σ(l)σ(m) with lcm(a,b,c) = 7,8 or 9

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EVALUATION OF THE CONVOLUTION SUMS ∑l+15m=nσ(l)σ(m) AND ∑3l+5m=nσ(l)σ(m) AND AN APPLICATION

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On the number of representations of an integer by certain quadratic forms in sixteen variables

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On the number of representations of certain quadratic forms in 20 and 24 variables

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Representations of an Integer by Some Quaternary and Octonary Quadratic Forms

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On the number of representations of certain quadratic forms in 8 variables

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A simple extension of Ramanujan-Serre derivative map and some applications

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EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS

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

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THE CONVOLUTION SUM $\sum\limits_{m<n/9}\sigma(m)\sigma(n-9m)$

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The convolution sum $\sum_{m<n/8} \sigma(m) \sigma(n-8m)$

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Q3077963

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EVALUATION OF THE CONVOLUTION SUMS ∑i+3j=nσ(i)σ3(j) AND ∑3i+j=nσ(i)σ3(j)

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Identifiers

DOI

10.1142/s1793042124500544

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6540617