Sheffer sequences with zeros on a line
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916916383186944 |
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| author | Cheon, G. -S. Forgács, T. Tran, K. |
| author_facet | Cheon, G. -S. Forgács, T. Tran, K. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sheffer sequences with zeros on a line Cheon, G. -S. Forgács, T. Tran, K. Number Theory Complex Variables 05A15, 05A40, 30C15, 30E15 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. |
| title | Sheffer sequences with zeros on a line |
| topic | Number Theory Complex Variables 05A15, 05A40, 30C15, 30E15 |
| url | https://arxiv.org/abs/2508.18229 |