Dirichlet Character - Construction Via Residue Classes

Construction Via Residue Classes

Dirichlet characters may be viewed in terms of the character group of the unit group of the ring Z/kZ, as extended residue class characters.

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    The construction of life is at present in the power of facts far more than convictions.
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    Every poem of value must have a residue [of language].... It cannot be exhausted because our lives are not long enough to do so. Indeed, in the greatest poetry, the residue may seem to increase as our experience increases—that is, as we become more sensitive to the particular ignitions in its language. We return to a poem not because of its symbolic [or sociological] value, but because of the waste, or subversion, or difficulty, or consolation of its provision.
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    Genocide begins, however improbably, in the conviction that classes of biological distinction indisputably sanction social and political discrimination.
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