Exponential sums and rectangular partitions |
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Authors: | A Duane Porter Nick Mousouris |
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Institution: | Mathematics Department University of Wyoming Laramie, Wyoming 82071 USA;Mathematics Department Humboldt State University Arcata, California 95521 USA |
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Abstract: | Let F denote a finite field with q=pf elements, and let σ(A) equal the trace of the square matrix A. This paper evaluates exponential sums of the form S(E,X1,…,Xn)e{?σ(CX1?XnE)}, where S(E,X1,…,Xn) denotes a summation over all matrices E,X1,…,Xn of appropriate sizes over F, and C is a fixed matrix. This evaluation is then applied to the problem of counting ranked solutions to matrix equations of the form U1?UαA+DV1?Vβ=B where A,B,D are fixed matrices over F. |
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