Abstract
Throughout this monograph we use the notation
where z is a complex number. We define the Dedekind eta function by the infinite product
The product converges normally for q in the unit disc or, equivalently, for z in the upper half plane ℍ={z∈ℂ∣Im(z)>0}. This means that the product of the absolute values |1−q n| converges uniformly for z in every compact subset of ℍ. The normal convergence of the product implies that η is a holomorphic function on ℍ and that η(z)≠0 for all z∈ℍ.
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© 2011 Springer-Verlag Berlin Heidelberg
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Köhler, G. (2011). Dedekind’s Eta Function and Modular Forms. In: Eta Products and Theta Series Identities. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16152-0_1
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DOI: https://doi.org/10.1007/978-3-642-16152-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16151-3
Online ISBN: 978-3-642-16152-0
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