English

A modular type formula for Euler infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$

Number Theory 2011-12-22 v2 Quantum Algebra

Abstract

The main goal of this paper is to give a modular type representation for the infinite product (1x)(1xq)(1xq2)(1xq3)...(1-x)(1-xq)(1-xq^2)(1-xq^3).... It is shown that this representation essentially contains the well-known modular formulae either for Dedekind's eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions and related series.

Keywords

Cite

@article{arxiv.0905.1343,
  title  = {A modular type formula for Euler infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$},
  author = {Changgui Zhang},
  journal= {arXiv preprint arXiv:0905.1343},
  year   = {2011}
}

Comments

29 pages