Ph.D. Program in Mathematics.Yıldırım, Cem Y.Karabulut, Yunus.2023-03-162023-03-162015.MATH 2015 K38 PhDhttps://digitalarchive.library.bogazici.edu.tr/handle/123456789/15326In this thesis, we focus on the vertical distribution problems of the zeros of the Riemann zeta-function and other related functions. In the rst half of our study we modify Montgomery's argument [1] in such a way that we can obtain some analogues of the pair correlation of zeta zeros, which provide some gap and multiplicity results. In the second half of our study we estimate the averages studied in [2] over the zeta maximas on the critical line instead of zeros so that we arrive at a result on the number of distinct zeta zeros.30 cm.Functions, Zeta.Number theory.x, 194 leaves ;