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Zeros of the constant term in the Chowla-Selberg formula

100%

Ki H.

Acta Arithmetica

2006

tom 124

nr 3

197-204

On the zeros of degree one L-functions from the extended Selberg class

72%

Ki H., Lee Y.

Acta Arithmetica

2011

tom 149

nr 1

23-36

Normal numbers and subsets of N with given densities

72%

Ki H., Linton T.

Fundamenta Mathematicae

1994

tom 144

nr 2

163-179

For X ⊆ [0,1], let $D_X$ denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of $D_X$. For α ≥ 3, X is properly $D_ξ(Π^0_α)$ iff $D_X$ is properly $D_ξ(Π^0_{1+α})$. We also show that for every nonempty set X ⊆[0,1], $D_X$ is $Π^0_3$-hard. For each nonempty $Π^0_2$ set X ⊆ [0,1], in particular for X = {x}, $D_X$ is $Π^0_3$-complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is $Π^0_3$-complete. Moreover, $D_ℚ$, the subsets of ℕ with rational densities, is $D_2(Π^0_3)$-complete.

Ograniczanie wyników

2 Acta Arithmetica

1 Fundamenta Mathematicae

3 Ki H.

1 Lee Y.

1 Linton T.

1 2011

1 2006

1 1994

Wyniki wyszukiwania

Zeros of the constant term in the Chowla-Selberg formula

On the zeros of degree one L-functions from the extended Selberg class

Normal numbers and subsets of N with given densities