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A Constructive theory of triple and quintuple product identities of the second degree

Authors: Richard Blecksmith, John Brillhart and Irving Gerst
Journal: Math. Comp. 67 (1998), 797-814
MSC (1991): Primary 11F11
MathSciNet review: 1458217
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Abstract: The groundwork for a theory of quadratic identities involving the classical triple and quintuple products is layed. The approach is through the study and use of affine maps that act on indexing lattices associated with the terms (double sums) in the given identity. The terms of the identity are found to be connected by the invariant of a ternary quadratic form.

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Additional Information

Richard Blecksmith
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115

John Brillhart
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Irving Gerst
Affiliation: Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, New York 11794

Keywords: Quadratic identities, triple product, quintuple product, invariant
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: December 11, 1996
Dedicated: Dedicated to the memory of our wonderful friend and colleague, Irving Gerst
Article copyright: © Copyright 1998 American Mathematical Society