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

DOI10.1007/s11139-023-00704-6arXiv2303.02921MaRDI QIDQ6164982

B. Ramakrishnan, Brundaban Sahu, Anup Kumar Singh

Publication date: 28 July 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.02921

zbMATH Keywords

convolution sumsmodular forms of integral weightsum of divisor functions

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Arithmetic functions; related numbers; inversion formulas (11A25) Hecke-Petersson operators, differential operators (one variable) (11F25)

Cites Work

• Some arithmetic identities involving divisor functions
• Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
• 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 and convolution sums
• 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)
• On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6
• EVALUATION OF THE CONVOLUTION SUMS ∑_l+15m=nσ(l)σ(m) AND ∑_3l+5m=nσ(l)σ(m) AND AN APPLICATION
• The convolution sum $\sum_{al+bm=n} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (1,14), (2,7), (1,7)$
• Convolution sums of a divisor function for prime levels
• 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)
• EVALUATION OF THE CONVOLUTION SUMS ∑_i+3j=nσ(i)σ₃(j) AND ∑_3i+j=nσ(i)σ₃(j)
• Evaluation of Convolution Sums entailing mixed Divisor Functions for a Class of Levels
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A simple extension of Ramanujan-Serre derivative map and some applications