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Let $\chi$ be the trivial Dirichlet character mod $N$. What is the primitive Dirichlet character associated to $\chi$? Is it just the character on $\mathbb{Z}$ that sends all integers to 1?

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Yes, exactly. :)

Here are more characters to meet the minimum.

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...and its Dirichlet generating function is that famous function of Riemann... – J. M. Dec 8 '11 at 0:58
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"more characters..." - was that a pun? – Gerry Myerson Dec 8 '11 at 2:01
"That would be telling..." – paul garrett Dec 8 '11 at 2:14
@Gerry ... to trigger the software... :) – paul garrett Dec 8 '11 at 2:16
Maaaaan.... this software situation is not ... useful... Sorry if my responses are [obstructed-by] ... – paul garrett Dec 8 '11 at 2:21

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