Harmonic analysis on the p-adic numbers
نویسنده
چکیده
The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian group, and (Qp, dp) is a complete metric space. (Qp, | · |p) is a complete nonarchimedean valued field. For x ∈ Qp, {x+ pZp : n ∈ Z}
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