Characters $\psi : G \to \mathbb{C}$ from abelian groups $G$ to the complex field $\mathbb{C}$ are well-known and appear all over. Is there an analogue for the $p$-adic complex numbers $\mathbb{C}_p$, that is, characters $G \to \mathbb{C}_p$? Do these obey similar properties such as an orthogonality relation as well as $|\psi(g)|_p = 1$? Could you please refer to me introductory material on this? Thanks a lot.
2026-04-01 20:21:53.1775074913
Characters with values on the $p$-adic complex field $\mathbb{C}_p$?
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