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Arthur Rubin (talk | contribs) Reverted 2 edits by 64.134.229.15 (talk): Revert more false statements and non-existant categories. (TW) |
"false" was too generous: this statement is not even wrong for any choice of p-adic field, let alone all at once |
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The roots of the Iwasawa logarithm log<sub>''p''</sub>(''z'') are exactly the elements of '''C'''<sub>''p''</sub> of the form ''p<sup>r''</sup>·ζ where ''r'' is a rational number and ζ is a root of unity.<ref>{{harvnb|Cohen|2007|loc=Proposition 4.4.45}}</ref>
Another major difference to the situation in '''C''' is that the ___domain of convergence of exp<sub>''p''</sub> is much smaller than that of log<sub>''p''</sub>. A modified exponential function — the [[Artin–Hasse exponential]] — can be used instead which converges on |''z''|<sub>''p''</sub> < 1.
==See also==
* [[Double exponential function]]
==Notes==
{{reflist}}
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==External links==
* {{planetmath reference|id=7000|title=p-adic exponential and p-adic logarithm}}
* [http://homes.esat.kuleuven.be/~fvercaut/talks/pAdic.pdf Efficient p-adic arithmetic] (slides)
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[[Category:Exponentials]]
[[Category:p-adic algorithms]]
[[Category:p-adic analysis]]
[[Category:p-adic arithmetic]]
[[Category:p-adic numbers]]
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