Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients

2013/02/10 by Alexander Berkovich, Berkovich, Alexander, Frank Patane +1
Mathematics · #11B65 #11E16 #11E20 #11E25 #11F11 #11F20 #11F27 #14K25 #1F03 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B65 #msc:11E16 #msc:11E20 #msc:11E25 #msc:11F11 #msc:11F20 #msc:11F27 #msc:14K25 #msc:1F03

paper · pdf · doi:10.48550/arxiv.1302.2359

27 pages

arxiv created 2013/08/16 · arxiv updated 2013/08/19

Abstract

We state and prove an identity which represents the most general eta-products of weight 1 by binary quadratic forms. We discuss the utility of binary quadratic forms in finding a multiplicative completion for certain eta-quotients. We then derive explicit formulas for the Fourier coefficients of certain eta-quotients of weight 1 and level 47, 71, 135,648 1024, and 1872.

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