Representation of Ramanujan's tau function by twisted divisor functions

Key Points

• The goal is to represent Ramanujan's tau function using twisted divisor functions and to construct cusp forms.
• Constructed identities through convolution sums of twisted divisor functions.
• Developed an infinite family of identities related to Ramanujan's tau function.
• Explicitly formed non-vanishing level 1 cusp forms from modular forms of higher levels.
• Established new representations of Ramanujan's tau function.
• Identified connections between twisted divisor functions and modular forms.
• Showed the construction of cusp forms contributes to understanding number theory.