Representation of Ramanujan's tau function by twisted divisor functions
Number Theory
2026-04-16 v1
Abstract
We present an infinite family of identities that represent Ramanujan's tau function in terms of convolution sums of twisted divisor functions. Our method involves explicitly constructing non-vanishing level cusp forms from modular forms of higher levels.
Keywords
Cite
@article{arxiv.2604.13365,
title = {Representation of Ramanujan's tau function by twisted divisor functions},
author = {Tianyu Ni},
journal= {arXiv preprint arXiv:2604.13365},
year = {2026}
}
Comments
12 pages, to appear in International Journal of Number Theory