Sheffer sequences with zeros on a line
Number Theory
2025-08-26 v1 Complex Variables
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.
Cite
@article{arxiv.2508.18229,
title = {Sheffer sequences with zeros on a line},
author = {G. -S. Cheon and T. Forgács and K. Tran},
journal= {arXiv preprint arXiv:2508.18229},
year = {2025}
}