p-adic exponential and p-adic logarithm
The domain of is restricted because the radius of convergence of the series over is precisely . Recall that, for , we define
where is the largest exponent such that divides . For example, if , then is defined over . However, is never defined, but is well-defined over (when , the number because ).
Proposition (Properties of and ).
With and defined as above:
If and are defined then .
if and only if is a rational power of times a root of unity.
, for all and .
In a similar way one defines the general -adic power by:
where it makes sense.
|Title||p-adic exponential and p-adic logarithm|
|Date of creation||2013-03-22 15:13:50|
|Last modified on||2013-03-22 15:13:50|
|Last modified by||alozano (2414)|
|Defines||general -adic power|