2. Function fields

Problem 2.1.
[S. Gonek] Develop a heuristic for moments of Lfunctions over function fields. Can one carry out the analogous ConreyKeating calculation for high moments (fixed $q$, large degree $g$)?
Remark. For this problem, it may be easier to start with low moments first.


Problem 2.2.
[H. Iwaniec] Consider a family of elliptic curves with a known rational point. Evaluate moments of $L$functions in this family at certain points. How does the fixed rational point analytically affect calculations? E.g. $y^2=x^3+ax+b^2$ with $a,b$ integers having $a,b\leq X$ (or in $\mathbb{F}_q[t]$). 
Problem 2.3.
[P. Humphries] Develop a heuristic for moments of Lfunctions of automorphic forms over function fields. What are families in this context? 
Problem 2.4.
[S. Gonek and J. Keating] Analyze Alexandra Floreaâ€™s formula for $V$ not equal to a square. 
Problem 2.5.
[S. Gonek and J. Keating] Evaluate moments of ratios of $L$functions over function fields.
Cite this as: AimPL: Moments of zeta and correlations of divisor sums, available at http://aimpl.org/zetamoments.