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## 2. Function fields

1. #### Problem 2.1.

[S. Gonek] Develop a heuristic for moments of L-functions over function fields. Can one carry out the analogous Conrey-Keating calculation for high moments (fixed $q$, large degree $g$)?
1. 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 L-functions of automorphic forms over function fields. What are families in this context?
• #### Problem 2.4.

[S. Gonek and J. Keating] Analyze Alexandra Florea’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.