Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Circles passing through five or more integer points

100%

Plunkett-Levin S.

Acta Arithmetica

2013

tom 158

nr 2

141-164

We find an improvement to Huxley and Konyagin's current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let $W_m(R)$ be the number of cyclic polygons with m integer point vertices centred in the unit square with radius r ≤ R. There exists a polynomial w(x) such that $W_mm ≥ (4^{m})/(m!) R^{2} w(log R)(1+o(1))$ where w(x) is an explicit polynomial of degree $2^{m-1}-1$.

Ograniczanie wyników

1 Acta Arithmetica

1 Plunkett-Levin S.

1 2013

Wyniki wyszukiwania

Circles passing through five or more integer points