1. CJM 2015 (vol 69 pp. 130)
 Levin, Aaron; Wang, Julie TzuYueh

On NonArchimedean Curves Omitting Few Components and their Arithmetic Analogues
Let $\mathbf{k}$ be an algebraically closed field complete with respect
to a nonArchimedean absolute value of arbitrary characteristic.
Let $D_1,\dots, D_n$ be effective nef divisors intersecting
transversally in an $n$dimensional nonsingular projective variety
$X$.
We study the degeneracy of nonArchimedean analytic maps from
$\mathbf{k}$ into $X\setminus \cup_{i=1}^nD_i$ under various geometric
conditions. When $X$ is a rational ruled surface and $D_1$ and
$D_2$ are ample, we obtain a necessary and sufficient condition
such that
there is no nonArchimedean analytic map from $\mathbf{k}$ into $X\setminus
D_1 \cup D_2$.
Using the dictionary between nonArchimedean Nevanlinna theory
and Diophantine approximation that originated in
earlier work with T. T. H. An, %
we also study arithmetic analogues of these problems, establishing
results on integral points on these varieties over $\mathbb{Z}$
or the ring of integers of an imaginary quadratic field.
Keywords:nonArchimedean Picard theorem, nonArchimedean analytic curves, integral points Categories:11J97, 32P05, 32H25 

2. CJM 2011 (vol 64 pp. 151)
 Miller, Steven J.; Wong, Siman

Moments of the Rank of Elliptic Curves
Fix an elliptic curve $E/\mathbb{Q}$ and assume the Riemann Hypothesis
for the $L$function $L(E_D, s)$ for every quadratic twist $E_D$ of
$E$ by $D\in\mathbb{Z}$. We combine Weil's
explicit formula with techniques of HeathBrown to derive an asymptotic
upper bound for the weighted moments of the analytic rank of $E_D$. We
derive from this an upper bound for the density of lowlying zeros of
$L(E_D, s)$ that is compatible with the random matrix models of Katz and
Sarnak. We also show that for any unbounded increasing function $f$ on $\mathbb{R}$,
the analytic rank and (assuming in addition the Birch and SwinnertonDyer
conjecture)
the number of integral points of $E_D$ are less than $f(D)$
for almost all $D$.
Keywords:elliptic curve, explicit formula, integral point, lowlying zeros, quadratic twist, rank Categories:11G05, 11G40 
