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Unformatted text preview: (3.5.3.7) we must show (Pk 1) ( 1)k mod p for Ogk<_p1 ~, (  t)k [p~f(1) dP e: f(2) (3.5.3.8) k+e=pl,e*0  Pk (f(2)) de e' f(1)] e dr(V, (gv) Reindexing the summation by k and re=Y1, (3.5.3.8) becomes (re membering that ( 1) k+l ( !) m mod p) ( 1) k nkf(1) dn"f(2) (3.5.3.9) k+m=pZ + ~ ( 1)"1Pk(f(2)) de'f(l)edF(V, (gv). k+m=p2 This is the case; in fact, the left member of (3.5.3.9) is (3.5.3.10) d( E (_ 1)kpk(f(1)) P'(f(2))). k+m=p2 This proves (3.5.0.3) in case b = 2, and gives a hint of the combinatorial rearrangements necessary in the general case. (3.5.4) We now turn to the general case. We adopt the convention that a product indexed by a subset of Z is to be taken in increasing order, and...
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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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