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

JOURNAL OF NUMBER THEORY

卷:135

Article

Berkovich, Alexander¹  Patane, Frank¹ 

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

关键词: Eta-quotients;    Binary quadratic forms;    Theta series;    Multiplicative functions;    Hecke operators;    Dissections of q-series;   

DOI  :  10.1016/j.jnt.2013.08.016

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free