标题： 线上有零点的谢弗序列 显示英文标题

标题： Sheffer sequences with zeros on a line

摘要： 我们扩展了Bump等人的一个结果，以表明一大类Sheffer序列的零点——可能除了有限个例外情况外——都位于一条垂直线上。我们将其中一个这样的序列通过缩放Mellin变换的乘积表示与黎曼zeta函数联系起来，类似于涉及广义Laguerre多项式的Mellin变换的乘积分解，该分解将Gamma函数和Meixner多项式作为因子。 显示英文摘要

摘要： 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.