Let $M$ be a finite-dimensional simple $\mathbb Q$ algebra and $\Lambda$ an order in $M$. Its zeta-function is defined as $$ Z(s)=\sum_{I}|\Lambda/I|^{-s}, $$ where the sum runs over all left ideals and $s$ is a complex number. In a series of 14 papers in the eighties, Bushnell and Reiner claimed that the sum converges for $Re(s)>1$ and that the zeta function extends meromorphically with a pole at $s=1$. Using completely different methods, I found that in the case of dimension 4 it converges for $Re(s)>2$ only and has a pole at $s=2$. The convergence part, by the way, is easily contradicted in the case $M=M_2({\mathbb Q})$ and $\Lambda= M_2({\mathbb Z})$, the respective algebras of $2\times 2$ matrices, you simply need to restrict to the principal ideals, where already you get a sum which diverges at $s=2$.

Now, am I overlooking a renormalisation here, or have they got it wrong in all these papers? (In the second case, they probably made a mistake in the first paper and copied it along.)

In the second case, is their entire approach damaged or is it a small problem which is easily repaired?