Vertical distribution problems in zeta-function theory

In 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. 1. Montgomery, H. L., "The Pair Correlation of Zeros of the Zeta Function", Analytic Number Theory (Proceedings of Symposia in Pure Mathematics), Vol. 24, pp. 181- 193, American Mathematical Society, Providence R.I., 1973. 2. Conrey, J. B., A. Ghosh and S. M. Gonek, "Simple Zeros of the Riemann Zeta- Function", Proceedings of the London Mathematical Society, Vol. 76, No. 3, pp. 497-522, 1998.