90
N.M. Katz:
0<(x)<l
(6.5.0.1)
x~ (x) modulo Z.
As real valued function, it satisfies
(x) =0r
((x)+(x))=(x+y)
(6.5.0.2)
(x)=(y)c~xy
mod Z
(x)+(x)=l
if xeZ.
(6.5.1)
For any prime number p, and any ~Qc~Zp
(i.e., any rational
number with denominator prime to p), we define Rp(a) to be the unique
integer
such that
O< Rp(~t)<=p I
(6.5.1.0)
= Rp (a) modulo p (Q r~ Zp).
As function from Q n Zp to {0, 1
.....
p 1 } = Z, it satisfies
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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