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

Chirre A.; Castañón O.V. · Ramanujan Journal (2022) · DOI: 10.1007/s11139-020-00321-7

Resumen

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.

Instituciones: Universidad Nacional de Ingeniería