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On the Number of Representations of Integers by Certain Quadratic Forms, II (pp. 153-182) $45.00
Authors:  Shaun Cooper
Abstract:
We investigate the number of representations of a positive integer by the quadratic form

λ1y21+λ2y22+λ3y23+λ4y24

where y1, y2, y3 and y4 are odd, positive integers, in the cases (λ1,λ2,λ3,λ4) = (1,1,1,3), (1,3,3,3), (1,2,2,3), (1,3,6,6), (1,3,4,4), (1,1,2,6) and (1,3,12,12). The development is, as much as possible, from first principles and relies on two classical identities from the theory of elliptic functions. A historical summary, going back to Eisenstein and Liouville, is included. 


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On the Number of Representations of Integers by Certain Quadratic Forms, II (pp. 153-182)