Let $\Lambda$ be a unimodular lattice in R^d. Then there are constants such that

$$\sum_{\gamma\in \Lambda, |\gamma|<R} \frac{1}{|\gamma|^d} = c_1 \log R + c_2 + o(1)$$

My question is : does $c_2$ depend on the lattice ? If yes, how ?

Let $\Lambda$ be a unimodular lattice in $\mathbb R^d$. Then there are constants such that

$$\sum_{\substack{\gamma\in \Lambda\\0<|\gamma|<R\\}} \frac{1}{|\gamma|^d} = c_1 \log R + c_2 + o(1).$$

My questions are: Does $c_2$ depend on the lattice ? If yes, how ?