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Unformatted text preview: p ( n )p ( n1)p ( n2) + p ( n5) + ... + (1) k p ( n1 2 k (3 k1))+ (1) k p ( n1 2 k (3 k + 1)) + ... = 0 . Using this identity compute the values of p ( n ) for n 20. 4.2 Prove the Gauss identity : 2 Y n =0 (1x 2 n +2 ) Y n =0 (1x 2 n +1 ) 1 = X r =0 x r ( r +1) / 2 . 4.3 Prove the Jacobi identity : Y n =1 (1x n ) 3 = X r =0 (1) r (2 r + 1) x r ( r +1) / 2 . 4.4 Using (4 . 2) prove the following identity about Gaussian sums : 1 q q1 X r =0 er 2 p/q = 1 p p1 X r =0 er 2 q/p . Here p,q are two coprime natural numbers.[Hint: Consider the assymptotic of the function f ( x ) = (0; ix + p q ) when x goes to zero.]...
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This note was uploaded on 01/08/2012 for the course MATH 300 taught by Professor Ontonkong during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 ONTONKONG
 Integers

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