Publication:
A note on the zeros of approximations of the Ramanujan Ξ -function
A note on the zeros of approximations of the Ramanujan Ξ -function
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Date
2020
Authors
Chirre A.
Castañón O.V.
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Publisher
Springer
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Abstract
In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ -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. © 2020, The Author(s).
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Keywords
Zeros of approximations of the Ramanujan Ξ -function,
Distribution of zeros of entire functions,
Ramanujan zeta function,
Riemann hypothesis