EVALUATION OF CONVOLUTION SUMS AND FOR k = a · b = 21, 33, AND 35

DOI10.1017/S0017089521000203zbMath1497.11017OpenAlexW3183498070MaRDI QIDQ5070184

Publication date: 11 April 2022

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089521000203

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)

Cites Work

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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Ramanujan's Eisenstein series of level 7 and 14
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
Eisenstein series in Ramanujan's Lost Notebook
Elliptic integrals and Ramanujan-type series for $1/\pi$ associated with ${\Gamma}_{0}(N)$, where $N$ is a product of two small primes
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
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)

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