Homogeneous additive equations

1963/08/13 by Harold Davenport, H. Davenport, D. J Lewis +1 · 8 citations
Mathematics · #Functional Equations Stability Results

paper · doi:10.1098/rspa.1963.0143

openalex publication_date 1963/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25

Abstract

Abstract An investigation into conditions under which an equation of the form c1xk1 + ... + csxks = 0 will have solutions in which x1 ..., xs are integers (not all 0).

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• Rational points on varieties defined by multihomogeneous diagonal forms
• Quartic Forms in Many Variables
• Random diophantine equations of additive type
• On Artin's conjecture: linear slices of diagonal hypersurfaces

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