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 | References | Similar Articles | Additional Information

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.

**1.**Richard Blecksmith, John Brillhart, and Irving Gerst,*On a certain (mod 2) identity and a method of proof by expansion*, Math. Comp.**56**(1991), no. 194, 775–794. MR**1068825**, 10.1090/S0025-5718-1991-1068825-2**2.**Richard Blecksmith, John Brillhart, and Irving Gerst,*A fundamental modular identity and some applications*, Math. Comp.**61**(1993), no. 203, 83–95. MR**1197509**, 10.1090/S0025-5718-1993-1197509-7**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:
http://dx.doi.org/10.1090/S0025-5718-98-00931-4

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

Article copyright:
© Copyright 1998
American Mathematical Society