A note on the zeros of approximations of the Ramanujan $\Xi-$function

Andr\'es Chirre; Oswaldo Vel\'asquez Casta\~n\'on

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A note on the zeros of approximations of the Ramanujan Xi-function

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arxiv 2004.14465 v1 pith:Z4HH72ED submitted 2020-04-29 math.NT math.CV

A note on the zeros of approximations of the Ramanujan Xi-function

Andr\'es Chirre , Oswaldo Vel\'asquez Casta\~n\'on This is my paper

classification math.NT math.CV

keywords zerosapproximationscertainfunctionramanujanapproachasquezcondition

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In this paper, we review the study of the distribution of the zeros of certain approximations for the Ramanujan $\Xi-$function given by Haseo Ki, and we provide a new proof of his results. Our approach is motivated by the ideas of Vel\'asquez in the study of the zeros of certain sums of entire functions with some condition of stability related to the Hermite-Biehler theorem.

A note on the zeros of approximations of the Ramanujan Xi-function

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