Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function

Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann Zeta function is discussed. Given a positive number, the function is equal to the increment taken by the continuous argument branch of the function as ranges along the segment joining certain points. Choosing an argument branch whose value at a certain point is zero and using stirling's formula for the gamma function, a certain result is obtained where the function is represented by the asymptotic series. Hutchinson's results showed that 'almost all' ordinates are separated from each other by Gram points, and this conjecture is known as Gram's law or Gram's rule. It was also conjectured that the exceptions from the Gram's rule are fairly rare and insignificant in the sense that it does not exceed a constant yet sufficiently large number.