2 problems

Let $A$ be an abelian variety of dimension $g$ over a field $k$ with $\operatorname{char}(k)\neq 2$, and let $\lambda\colon A\to A^\vee$ be a principal polarization. For each…

Let $n$ and $e$ be positive integers, let $\nu(n)$ denote the exponent in the highest power of $2$ dividing $n$, and let $\alpha(n)$ denote the number of ones in the dyadic expansi…