Article:
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B. Heim, M. Neuhauser & F. Rupp (2018): Imaginary Powers of the Dedekind Eta Function,
Experimental Mathematics, DOI: 10.1080/10586458.2018.1468288.

published online: 04 Jun 2018

URL: https://www.tandfonline.com/doi/full/10.1080/10586458.2018.1468288


Abstarct:
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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.

Keywords:
Fourier coefficients, Euler products, integer-valued polynomials, Lehmer conjecture,
roots of polynomials

2010 AMS subject classification:
Primary 26C10, 11F20, Secondary 11F30, 11F37, 12D10