Abstract
In many applications of elliptic modular functions to number theory the eta function plays a central role. It was introduced by Dedekind in 1877 and is defined in the half-plane H = {τ: Im(τ) > 0} by the equation
The infinite product has the form Π (1 — xn) where x = e2πiτ. If τ∈H then |x| < 1 so the product converges absolutely and is nonzero. Moreover, since the convergence is uniform on compact subsets of H, η(τ) is analytic on H.
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© 1990 Springer Science+Business Media New York
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Apostol, T.M. (1990). The Dedekind eta function. In: Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0999-7_3
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DOI: https://doi.org/10.1007/978-1-4612-0999-7_3
Publisher Name: Springer, New York, NY
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