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A Multiple Exponential Sum to Modulus p2

Published online by Cambridge University Press:  20 November 2018

D. R. Heath-Brown
D. R. Heath-Brown*
Affiliation:
Magdalen CollegeOxford 0X1 4AU, England
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Abstract

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For suitable polynomials f(x) ∊ ℤ[x] in n variables, of total degree d, it is shown that

This is, formally, a precise analogue of a theorem of Deligne [1] on exponential sums (mod p). However the proof uses no more than elementary algebraic geometry.

Keywords

10G10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 394 - 396
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Deligne, P., La conjecture de Weil. I. Publications Mathématiques 43, Institue des Hautes Études Scientifiques, Paris, 1974, pp. 273–307.Google Scholar
2. Shafarevich, I.R., Basic algebraic geometry, Grundlehren der mathematischen Wissenchaften 213, Springer, New York, 1974.Google Scholar