2025/08/25 by Cheon, G. -S., Forgács, T., Tran, K.
#05A15 #05A40 #30C15 #30E15 #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2508.18229
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.