There is now a preliminary conjecture for the lower
order terms of the above article in the case of integral moments.
However, it would be interesting to have the lower order terms for fractional
moments as well. For example, we expect that

What would be the expected error term here? Are there more main terms? It may not be unreasonable to guess that for this example there will be an (infinite) asymptotic series of powers of so that

holds for any with some sequence of . Is there some way to guess this answer? A good conjecture could easily be tested numerically.

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