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Sums of m-th powers in p-adic rings

Published online by Cambridge University Press:  26 February 2010

C. P. Ramanujam
C. P. Ramanujam
Affiliation:
Tata Institute of Fundamental Research, Bombay
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Extract

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 8m5m-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.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 2 , December 1963 , pp. 137 - 146
Copyright
Copyright © University College London 1963

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References

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