Mathematics of Computation

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

Author(s): Richard Blecksmith; John Brillhart; Irving Gerst.
Journal: Math. Comp. 67 (1998), 797-814.
MSC (1991): Primary 11F11
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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.

References:

1.: R. Blecksmith, J. Brillhart, and I. Gerst, On a certain (mod 2) identity and a method of proof by expansion, Math. Comp. 56 (1991), 775-794. MR 91j:11087
2.: R. Blecksmith, J. Brillhart, and I. Gerst, A fundamental modular identity and some applications, Math. Comp. 61 (1993), 83-95. MR 94c:11100
3.: E. B. Elliot, An Introduction to the Algebra of Quantics, Second Edition, Chelsea, New York, 1969.
4.: H. J. S. Smith, On systems of linear indeterminant equations and congruences, Collected Math. Papers 1 (1965), 367-409.

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Additional Information:

Richard Blecksmith
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
Email: richard@math.niu.edu

John Brillhart
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: jdb@math.arizona.edu

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

DOI: 10.1090/S0025-5718-98-00931-4
PII: S 0025-5718(98)00931-4
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
Copyright of article: Copyright 1998, American Mathematical Society


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