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

DOI10.5666/KMJ.2019.59.3.377zbMath1455.11011arXiv1607.06039MaRDI QIDQ5215882

Şaban Alaca, Ayşe Alaca, Ebénézer Ntienjem

Publication date: 13 February 2020

Full work available at URL: https://arxiv.org/abs/1607.06039

zbMATH Keywords

Eisenstein seriesrepresentationsmodular formscusp formsDedekind eta functionconvolution sumssum of divisors functioneta quotientsoctonary 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) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (4)

A simple extension of Ramanujan-Serre derivative map and some applications ⋮ Evaluation of certain convolution sums involving the sum of the divisors function ⋮ Unnamed Item ⋮ On the number of representations of certain quadratic forms in 8 variables

Uses Software

• Maple

Cites Work

• Unnamed Item
• Unnamed Item
• Powers of theta functions
• Quintic and septic Eisenstein series
• Eta Products and Theta Series Identities
• 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)
• EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS
• 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
• Modular Forms
• Evaluation of two convolution sums involving the sum of divisors function
• REPRESENTATIONS BY CERTAIN OCTONARY QUADRATIC FORMS WHOSE COEFFICIENTS ARE 1, 2, 3 AND 6

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