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Unformatted text preview: =1 ( n ) q log(2 M + 1) + q q log q and deduce that N n =1 ( n ) q log q holds for every N N . (e) Prove that for n N , d ( n ) 2 n . (f) Assume now that is a character modulo q induced by the primitive character modulo modulo r , so that r is the conductor of and r  q . Prove that N n =1 ( n ) = N n =1 ( n,q/r )=1 ( n ) = d  q/r ( d ) ( d ) m N/d ( m ) and that N n =1 ( n ) 2 q log q (the P olyaVinogradov inequality)....
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 Spring '08
 Vaughan,R
 Number Theory

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