In the book "The arithmetic of elliptic curves" by Silverman, I try to solve the exercise 6.2. It is used in the proof for the convergence of the Eisenstein series. I did the first question (all parallelogram for a lattice has the same area). I don't how to do the second and third question.
Q2 : For R $\rightarrow \infty$, $\#\{\omega \in \Lambda : | \omega | \leqslant R \} = \pi R^2/A+O(R)$.
A is the area of the fundamental parallelogram.
Q3 : It exists $c$ such that for all $R > 0 $ $\#\{\omega \in \Lambda : | R \leqslant | \omega |< R+1 \} <cR$
Cordially, doeup
