New proofs of two identities of Ramanujan

Patrick Morton

New proofs of two identities of Ramanujan

Number Theory 2024-01-12 v2

Authors: Patrick Morton

Abstract

A proof of several identities of Ramanujan involving theta functions of level $7$ is given which uses a specific modular function for $\Gamma_1(7)$ and Klein's projective representation of $PSL(2,7)$ into $PSL(3, \mathbb{C})$ . Four identities of Berndt and Zhang are derived as algebraic corollaries of the main proof.

Keywords

ramanujan identities theta functions modular function klein representation psl(2,7) algebraic corollaries

Cite

@article{arxiv.2303.18140,
  title  = {New proofs of two identities of Ramanujan},
  author = {Patrick Morton},
  journal= {arXiv preprint arXiv:2303.18140},
  year   = {2024}
}

Comments

20 pages. Section 4 has been added, giving corollaries of the main proof. Title has been modified

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