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 Jm (A) be the subring of A generated by the m-th powers of elements of A. We will prove that any element of Jm (A) is a sum of at most 8m5 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Cambridge University Press. |
| ID Code: | 82926 |
| Deposited On: | 15 Feb 2012 12:28 |
| Last Modified: | 15 Feb 2012 12:28 |
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