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arXiv · 2508.18229

Sheffer sequences with zeros on a line

G. -S. Cheon·T. Forgács·K. Tran
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Abstract

We extend a result of Bump et al. to show that a large family of Sheffer sequences has their zeros - up to perhaps a finite number of exceptions - on a vertical line. We connect a particular such sequence to the Riemann zeta function via a product representation of a scaled Mellin transform, analogously to the product decomposition of a Mellin transform involving the generalized Laguerre polynomials into factors of the Gamma function and Meixner polynomials.

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BibTeXRIS

G. -S. Cheon, T. Forgács, K. Tran. 2025-08-25. Sheffer sequences with zeros on a line. https://arxiv.org/abs/2508.18229

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