Sign Changes of the Ramanujan $$\tau $$-Function

Heim, Bernhard; Neuhäuser, Markus

doi:10.1007/978-981-15-8719-1_7

Springer Proceedings in Mathematics &Amp; Statistics

2020

DOI: 10.1007/978-981-15-8719-1_7

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Sign Changes of the Ramanujan $$\tau $$-Function

Bernhard Heim

Markus Neuhäuser

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2023

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Cited by 1 publication

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Zeros transfer for recursively defined polynomials

Heim,

Neuhauser,

Tröger

2023

Res. number theory

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The zeros of D’Arcais polynomials, also known as Nekrasov–Okounkov polynomials, dictate the vanishing of the Fourier coefficients of powers of the Dedekind eta functions. These polynomials satisfy difference equations of hereditary type with non-constant coefficients. We relate the D’Arcais polynomials to polynomials satisfying a Volterra difference equation of convolution type. We obtain results on the transfer of the location of the zeros. As an application, we obtain an identity between Chebyshev polynomials of the second kind and 1-associated Laguerre polynomials. We obtain a new version of the Lehmer conjecture and bounds for the zeros of the Hermite polynomials.

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Zeros transfer for recursively defined polynomials

Heim,

Neuhauser,

Tröger

2023

Res. number theory

View full text Add to dashboard Cite

show abstract

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Sign Changes of the Ramanujan $$\tau $$-Function

Cited by 1 publication

References 19 publications

Zeros transfer for recursively defined polynomials

Zeros transfer for recursively defined polynomials

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