The Ramanujan Journal

, Volume 48, Issue 1, pp 1–11 | Cite as

Fourier coefficients of powers of the Dedekind eta function

  • Bernhard HeimEmail author
  • Markus Neuhauser
  • Florian Rupp


In this paper, we study the vanishing properties of Fourier coefficients of rth powers of the Dedekind eta function. We give a certain type of classification of this property based on r. Further we extend the results of Atkin, Cohen, and Newman for odd powers. This leads to a partial answer to a question raised by van Lint. We also indicate possible generalization of the Lehmer conjecture.


Fourier coefficients Euler products Dedekind eta function Lehmer conjecture 

Mathematics Subject Classification

Primary 05A17 11F20 Secondary 11F30 11F37 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.German University of Technology in OmanMuscatSultanate of Oman

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