2009/05/08 by Changgui Zhang, Zhang, Changgui
Mathematics · #05A30 #11F20 #11F27 #30D05 #33E05 #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #math.NT #math.QA #msc:05A30 #msc:11F20 #msc:11F27 #msc:30D05 #msc:33E05
paper · pdf · doi:10.48550/arxiv.0905.1343
29 pages
arxiv created 2011/12/21 · arxiv updated 2011/12/22
The main goal of this paper is to give a modular type representation for the infinite product (1-x)(1-xq)(1-xq2)(1-xq3).... 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.