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Sparsity of the intersection of polynomial images of an interval

100%

Chang M.-C.

Acta Arithmetica

2014

tom 165

nr 3

243-249

We show that the intersection of the images of two polynomial maps on a given interval is sparse. More precisely, we prove the following. Let $f(x),g(x) ∈ 𝔽_{p}[x]$ be polynomials of degrees d and e with d ≥ e ≥ 2. Suppose M ∈ ℤ satisfies $p^{1/E(1 + κ/(1-κ)} > M > p^ε$, where E = e(e+1)/2 and κ = (1/d - 1/d²) (E-1)/E + ε. Assume f(x)-g(y) is absolutely irreducible. Then $|f([0,M]) ∩ g([0, M])| ≲ M^{1-ε}$.

Short character sums with Fermat quotients

88%

Chang M.-C.

Acta Arithmetica

2012

tom 152

nr 1

23-38

Ograniczanie wyników

2 Acta Arithmetica

2 Chang M.-C.

1 2014

1 2012

Wyniki wyszukiwania

Sparsity of the intersection of polynomial images of an interval

Short character sums with Fermat quotients