0
$\begingroup$

At the beginning of Haruzo Hida's article "Big Galois representations and $p$-adic L functions", he has defined $$\chi_1= \textrm{the } N_0 \textrm{-part of} \chi \times \textrm{the tame } p\textrm{-part of} \chi.$$ Here $N_0$ is an integer prime to $p$ and $\chi$ is a Dirichlet character modulo $N_0p^r$.

So does that mean $\chi_1=\chi\vert_{(\mathbb{Z}/N_0)^\ast\times\mathbb{Z}/(p-1)\mathbb{Z}}$?

$\endgroup$
2
  • 1
    $\begingroup$ Where did you encounter the terminology? That reference, and its references in turn, is where you should start. $\endgroup$
    – LSpice
    Sep 10, 2019 at 0:48
  • 1
    $\begingroup$ With $a\frac{N_0}{p^r}+bp^r=1$ It is probably $n \mapsto\chi(bp^r+a\frac{N_0}{p^r} n^{ p^{r-1}})$ $\endgroup$
    – reuns
    Sep 10, 2019 at 1:13

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.