# Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC?

Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC?

It seems, judging by the abstract of a 2002 paper of Ram Murty and a possibly Romanian co-author published on www.degruyter.com, that Selberg's orthonormality conjecture (SOC for short) is essentially equivalent to the analogue of Montgomery's pair correlation conjecture for the whole Selberg class. So, Would a proof of both (G)RH (say, for the Riemann Zeta function only, or for the whole Selberg class) and Montgomery's pair correlation conjecture (once again, for the Riemann Zeta function only, or for the whole Selberg class) imply SOC? Thanks in advance for any reference and/or insight.

• Are you referring to Murty and Zaharescu, Explicit formulas for the pair correlation of zeros of functions in the Selberg class, Forum Math., Vol. 14, 2002, no. 1, 65-83? This is item 92 at mast.queensu.ca/~murty/index2.html – Gerry Myerson Aug 2 '13 at 0:58
• Type $$\rm how\ to\ read\ dvi\ files$$ into Google. – Gerry Myerson Aug 3 '13 at 12:08