Imaginary powers of the Dedekind eta function

Heim, Bernhard; Neuhauser, Markus; Rupp, Florian

doi:10.1080/10586458.2018.1468288

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Imaginary powers of the Dedekind eta function

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Heim, Bernhard
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1080/10586458.2018.1468288
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Heim-Neuhauser-Rupp_Imaginary powers of the Dedekind eta function_Preprint.pdf
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Citation

Heim, B., Neuhauser, M., & Rupp, F. (2020). Imaginary powers of the Dedekind eta function. Experimental Mathematics, 29(3), 317-325. doi:10.1080/10586458.2018.1468288.

Cite as: https://hdl.handle.net/21.11116/0000-0005-1EE3-A

Abstract

In this article, complex powers of the Dedekind eta function are studied. The vanishing of the nth Fourier coefficients are labeled by the roots of an attached polynomial pn(x). We study these polynomials, and their values and roots distribution. The considered polynomials of degree n ⩽ 700 are verified as Hurwitz polynomials. We study the value distribution of the polynomials restricted to the imaginary axis.