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Simultaneous diagonal p–adic equations

Part of: Diophantine equations

Published online by Cambridge University Press:  26 February 2010

I. D. Meir
I. D. Meir
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH. Tricorder Technology plc, The Long Room, Coppermill Lock, Summerhouse Lane, Harefield, Middlesex UB9 6JA.
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Abstract

It is known that a system of r additive equations of degree k with greater than 2rk variables has a non-trivial p-adic solution for all p > k2r + 2. In this paper we consider the same system with more than crk variables, c > 2, and show the existence of a non-trivial solution for all p > r2k2+(2/(c − 2)) if r ≠ 1 and p > k2+(2/(c − 1)) if r = 1.

MSC classification

Secondary: 11D79: Congruences in many variables
Type
Research Article
Information
Mathematika , Volume 45 , Issue 2 , December 1998 , pp. 337 - 349
Copyright
Copyright © University College London 1998

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References

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