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Displaying similar documents to “Some uniqueness results on meromorphic functions sharing two or three sets”

Convex meromorphic mappings

Albert E. Livingston (1994)

Annales Polonici Mathematici

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We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.

Hausdorff dimension and measures on Julia sets of some meromorphic maps

Krzysztof Barański (1995)

Fundamenta Mathematicae

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We study the Julia sets for some periodic meromorphic maps, namely the maps of the form f ( z ) = h ( e x p 2 π i T z ) where h is a rational function or, equivalently, the maps ˜ f ( z ) = e x p ( 2 π i h ( z ) ) . When the closure of the forward orbits of all critical and asymptotic values is disjoint from the Julia set, then it is hyperbolic and it is possible to construct the Gibbs states on J(˜f) for -α log |˜˜f|. For ˜α = HD(J(˜f)) this state is equivalent to the ˜α-Hausdorff measure or to the ˜α-packing measure provided ˜α is greater or smaller...

Zeros of Dirichlet L-series on the critical line

Peter J. Bauer (2000)

Acta Arithmetica

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Introduction. In 1974, N. Levinson showed that at least 1/3 of the zeros of the Riemann ζ-function are on the critical line ([19]). Today it is known (Conrey, [6]) that at least 40.77% of the zeros of ζ(s) are on the critical line and at least 40.1% are on the critical line and are simple. In [16] and [17], Hilano showed that Levinson's original result is also valid for Dirichlet L-series. This paper is a shortened version of parts of the dissertation [3], the full...

On addition of two distinct sets of integers

Vsevolod F. Lev, Pavel Y. Smeliansky (1995)

Acta Arithmetica

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What is the structure of a pair of finite integers sets A,B ⊂ ℤ with the small value of |A+B|? We answer this question for addition coefficient 3. The obtained theorem sharpens the corresponding results of G. Freiman.