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Question about padic number 
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#1
Aug2608, 01:00 PM

P: 42

1.Why the object requires prime number p?
2.Why the padic norm of x is defined by [tex]x_{p}=p^{m}[/tex]([tex]x=\frac{p^{m}r}{s}[/tex]),not [tex]x_{p}=p^{m}[/tex]? 3.[tex]Q_{p}\subset R[/tex] or [tex]R \subset Q_{p}[/tex]? 4.What is the difference between padic and ladic? what is the letter "l" stands for? 


#2
Aug2708, 05:50 PM

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P: 2,020

All of your questions are answered on Wikipedia's page on padic numbers.



#3
Aug2708, 05:56 PM

P: 532

2) the alternative you suggest wouldn't satisfy x+y<=x+y, so it isn't a norm. 3) neither. Q < R and Q < Q_p. 4) ladic is the same as padic, if l=p ! l is just some prime number. 


#4
Sep1708, 12:15 PM

P: 42

Question about padic number
Thank you.
One more question here is: What is the relationship between padic field and Galois field? 


#5
Sep1708, 06:52 PM

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P: 3,682




#6
Sep1808, 03:04 AM

P: 193

can you define a padic integral of any function f(x) where x is always a padic number
Can you define a padic differentiation ? in similar manner Is there any relationship between the qanalogue of a function and the padic set of numbers? 


#7
Jan2609, 03:13 PM

P: 41

In arithmetic geometry, one usually uses the letter, p, to denote the characteristic of a base field and "l" for a prime number different from the char.
For example, ladic etale cohomology. padic crystalline cohomology. 


#8
Jan2609, 03:19 PM

P: 41

i once heard a guy talking about galois fields. I asked him what the heck it was. he said it is a finite field.
So, if a finite field has q elements, then q is a power of some prime p. there is a subfield F_p in it. Z_p=inv.lim. F_p^n. 


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