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Eta Products of Weight \(\frac{1}{2}\) and \(\frac{3}{2}\)

  • Günter Köhler
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In Example 3.12 we learned that there are exactly six holomorphic eta products of weight \(\frac{1}{2}\) which are new for the levels 1, 2 or 4. In Sects. 1.1 and 1.2 we obtained series expansions for four of these functions. In a closing remark in Sect. 3.6 we explained that these expansions are simple theta series for the rational number field with Dirichlet characters. Now we derive similar expansions for the remaining two eta products
$$\eta^2(2z)/\eta(z) \hspace{8mm} \mbox{and} \hspace{8mm} \eta(z)\eta(4z)/\eta(2z) .$$

Keywords

Rational Number Modular Form Jacobi Identity Theta Series Dirichlet Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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