FYI: 'NOTES ON PAIR CORRELATION OF ZEROS AND PRIME NUMBERS' by Prof. D. A. GOLDSTON,

"These notes are based on my four lectures given at the Newton Institute in April 2004 during

the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpose

is to introduce the reader to the analytic number theory necessary to understand Montgomery’s

work on the pair correlation of the zeros of the Riemann zeta-function and subsequent work on

how this relates to prime numbers. A very brief introduction to Selberg’s work on the moments

of S(T) is also given."

Source Link:

https://arxiv.org/pdf/math/0412313.pdf.

Enjoy!

Relevant Reference Link:

'Montgomery's Pair Correlation Conjecture',

https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture.