# The integral of $\exp(i \lambda S(t))$

In the paper [CMP 1 794 265] by Keating and Snaith, the authors conjecture (see equation (100)) that

where may be expressed as an absolutely convergent product over primes and G is the Barnes double gamma function.

If is an integer, then the main term is 0. If is not an integer, then no instance of this remarkable formula has been proven (or even conjectured) before.

Back to the main index for L-functions and Random Matrix Theory.