💾 Archived View for satch.xyz › notes › dirichlet.gmi captured on 2023-06-14 at 14:10:14. Gemini links have been rewritten to link to archived content

-=-=-=-=-=-=-

p-adic representations of mod-5 Dirichlet Characters


	-390/1562  <==> 0, 1, 1, 1, 1
	-540/1562  <==> 0, 1,-1,-1, 1
	-1115/1562 <==> 0, 1,-i, i,-1
	-1215/1562 <==> 0, 1, i,-i, -1

Dividing numerators by five,

Here are the actual p-adic representations:

0+p+ p^2+ p^3+ p^4+...
0+p+3p^2+3p^3+ p^4+...
0+p+4p^2+2p^3+3p^4+...
0+p+2p^2+4p^3+3p^4+...

Numerators base five: