Ramanujam, C. P.
(1963)
*Sums of m-th powers in p-adic rings*
Mathematika, 10
(2).
pp. 137-146.
ISSN 0025-5793

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S002557930000406X

## Abstract

Let A be a complete discrete valuation ring of characteristic zero with finite residue field, and for any integer m > 1, let J_{m} (A) be the subring of A generated by the m-th powers of elements of A. We will prove that any element of J_{m} (A) is a sum of at most 8m^{5} m-th powers of elements of A. We will also prove a similar assertion when the residue field of A is only assumed to be perfect and of positive characteristic, with the number Γ(m) of summands depending only on m and not on A.

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ID Code: | 82926 |

Deposited On: | 15 Feb 2012 12:28 |

Last Modified: | 15 Feb 2012 12:28 |

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