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), 671675
MSC (1991):
Primary 11P05, 11R04, 15A33; Secondary 11C20, 11E25, 15A24
Published electronically:
July 6, 1999
MathSciNet review:
1646194
Fulltext PDF Free Access
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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.
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Additional Information
S. A. Katre
Affiliation:
Department of Mathematics, University of Pune, Pune411007, India
Email:
sakatre@math.unipune.ernet.in
Sangita A. Khule
Affiliation:
Department of Mathematics, University of Pune, Pune411007, India
DOI:
http://dx.doi.org/10.1090/S0002993999052065
PII:
S 00029939(99)052065
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
