Lipschitz<sup>2</sup>
: A New Version of an Old Principle

Spain, Philip

doi:10.1112/blms/27.6.565

Cited by 7 publications

(9 citation statements)

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“…1} is bounded and has Lipschitz parametrisable boundary, hence is Jordan measurable (see [42]). As the intersection of two Jordan measurable sets is Jordan measurable, we find that x p = c p }.…”

Section: Rational Pointsmentioning

confidence: 99%

Failures of weak approximation in families

Bright

Browning²,

Loughran³

2016

Compositio Math.

254

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Section: Rational Pointsmentioning

confidence: 99%

Failures of weak approximation in families

Bright

Browning²,

Loughran³

2016

Compositio Math.

254

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show abstract

“…The vast majority of such results is asymptotic in nature, which is not sufficient for our purposes. Explicit bounds on the number of lattice points in convex bodies can be found for instance in [17] and [20], however these bounds are, although quite general in the choice of the convex body, depend on parameters which are hard to compute. The advantage of bounds developed here in sections 3 and 4 is that they are reasonably sharp and easy to use in the particular case needed for our main result.…”

Section: Applying Corollary 41 We See That For Anymentioning

confidence: 99%

Integral Points of Small Height Outside of a Hypersurface

Fukshansky

2005

Mh Math

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Abstract. Let F be a non-zero polynomial with integer coefficients in N variables of degree M . We prove the existence of an integral point of small height at which F does not vanish. Our basic bound depends on N and M only. We separately investigate the case when F is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel's Lemma as well as to Faltings' version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem.

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“…. , z l ,z l are zeros of the polynomial g(z) := r 0 + r 1 z + · · · + r k+2l−1 z k+2l−1 + s k+2l z k+2l + · · · + s n z n , see (33). Thus for some t ′ 0 , .…”

Section: Proof Of Theorems 53mentioning

confidence: 95%