Rankin-Cohen Brackets and van der Pol-Type Identities for the Ramanujan's Tau Function

2007/11/22 by Ramakrishnan, B., Sahu, Brundaban
#11A25 #11F11 #11F25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0711.3512

Abstract

We use Rankin-Cohen brackets for modular forms and quasimodular forms to give a different proof of the results obtained by D. Lanphier and D. Niebur on the van der Pol type identities for the Ramanujan's tau function. As consequences we obtain convolution sums and congruence relations involving the divisor functions.

Related

• Rankin-Cohen brackets on quasimodular forms
• On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function
• Dirichlet series of Rankin-Cohen Brackets
• Rankin-Cohen brackets for Calabi-Yau modular forms
• Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions