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A note on the zeros of approximations of the Ramanujan $$\Xi $$ Ξ -function
The Ramanujan Journal ( IF 0.6 ) Pub Date : 2020-08-28 , DOI: 10.1007/s11139-020-00321-7
Andrés Chirre , Oswaldo Velásquez Castañón

In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan \(\Xi \)-function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach is motivated by the ideas of Velásquez (J Anal Math 110:67–127, 2010) in the study of the zeros of certain sums of entire functions with some condition of stability related to the Hermite–Biehler theorem.



中文翻译:

关于Ramanujan $$ \ Xi $$ function函数的逼近零的注记

在本文中,我们回顾了Ki给出的Ramanujan \(\ Xi \) -函数某些近似零的分布的研究(Ramanujan J 17(1):123–143,2008),并提供了新的证明他的结果。Velásquez(J Anal Math 110:67–127,2010)的思想在研究与Hermite–Biehler定理相关的某些稳定条件下的某些整体函数之和的零点时,激发了我们的方法。

更新日期:2020-08-29
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