Matrices over orders in algebraic number fields

as sums of -th powers

Authors:
S. A. Katre and Sangita A. Khule

Journal:
Proc. Amer. Math. Soc. **128** (2000), 671-675

MSC (1991):
Primary 11P05, 11R04, 15A33; Secondary 11C20, 11E25, 15A24

DOI:
https://doi.org/10.1090/S0002-9939-99-05206-5

Published electronically:
July 6, 1999

MathSciNet review:
1646194

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Abstract | References | Similar Articles | Additional Information

Abstract: David R. Richman proved that for every integral matrix is a sum of seven -th powers. In this paper, in light of a question proposed earlier by M. Newman for the ring of integers of an algebraic number field, we obtain a discriminant criterion for every matrix over an order of an algebraic number field to be a sum of (seven) -th powers.

**1.**M. Newman, Sums of squares of matrices, Pacific J. Math. 118 (1985), 497-506. MR**86k:15011****2.**D. R. Richman, The Waring problem for matrices, Linear and Multi. Alg. 22(1987), 171-192.MR**89d:11087****3.**L. N. Vaserstein, Every integral matrix is a sum of three squares, Linear and Multi. Alg. 20(1986), 1-4.MR**88e:15009****4.**L. N. Vaserstein, On the sum of powers of matrices, Linear and Multi. Alg. 21 (1987), 261-270. MR**89a:15016**

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Additional Information

**S. A. Katre**

Affiliation:
Department of Mathematics, University of Pune, Pune-411007, India

Email:
sakatre@math.unipune.ernet.in

**Sangita A. Khule**

Affiliation:
Department of Mathematics, University of Pune, Pune-411007, India

DOI:
https://doi.org/10.1090/S0002-9939-99-05206-5

Keywords:
Algebraic number fields,
order,
sums of powers,
discriminant,
matrices

Received by editor(s):
April 21, 1998

Published electronically:
July 6, 1999

Dedicated:
Dedicated to the memory of David R. Richman

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society