The density of zeros of forms for which weak approximation fails
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- by D. R. Heath-Brown PDF
- Math. Comp. 59 (1992), 613-623 Request permission
Abstract:
The weak approximation principle fails for the forms ${x^3} + {y^3} + {z^3} = k{w^3}$ , when $k = 2$ or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these forms. Evidence, both numerical and theoretical, is presented, which suggests that, for forms of the above type, the product of the local densities still gives the correct global density.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp. 59 (1992), 613-623
- MSC: Primary 11G35; Secondary 11D25, 11P55
- DOI: https://doi.org/10.1090/S0025-5718-1992-1146835-5
- MathSciNet review: 1146835