ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11R, 11C Katre, Shashikant A., University of Pune, India; Khule Sangita A., University of Pune, India Matrices over orders in algebraic number fields as sums of k-th powers David R. Richman proved that for n ≥ k ≥ 2 every integral n × n matrix is a sum of seven k-th powers. In this paper, we, in the light of a question raised earlier by M. Newman for the ring of integers of an algebraic number field, obtain a discriminant criterion for every n×n matrix (n ≥ k ≥ 2) over an order of an algebraic number field to be a sum of (seven) k-th powers. References:

1. M. Newman, Sums of squares of matrices, Pacific J. Math. 118 (1985),497-506.

2. D. R. Richman, The Waring problem for matrices, Linear and Multi. Alg. 22(1987).171-192