Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Matrices over orders in algebraic number fields
as sums of $k$-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
Published electronically: July 6, 1999
MathSciNet review: 1646194
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: David R. Richman proved that for $n \geq k \geq 2$ every integral $n \times n$ matrix is a sum of seven $k$-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 $n \times n$ matrix $ (n \geq k \geq 2)$ over an order of an algebraic number field to be a sum of (seven) $k$-th powers.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11P05, 11R04, 15A33, 11C20, 11E25, 15A24

Retrieve articles in all journals with MSC (1991): 11P05, 11R04, 15A33, 11C20, 11E25, 15A24


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: http://dx.doi.org/10.1090/S0002-9939-99-05206-5
PII: S 0002-9939(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