Integral points on strictly convex closed curves
A negative answer is given to Swinnerton-Dyer's question: Is it true that for any ε > 0 there exists a positive integer n such that for any planar closed strictly convex n-times differentiable curve Γ, when it is blown up a sufficiently large number ν of times, the number of integral points on the resultant curve will be less than νɛ. An example has been constructed when this number for an infinite number ν is not less than ν1/2, while Γ is infinitely differentiable.
KeywordsPositive Integer Infinite Number Integral Point Negative Answer Closed Curf
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