The Exponent of Convergence for 2-Dimensional Jacobi-Perron Type Algorithms

2001 ◽  
Vol 132 (2) ◽  
pp. 141-152 ◽  
Author(s):  
Kentaro Nakaishi
Keyword(s):  
Exponent Of Convergence

scholarly journals Value distribution of meromorphic functions concerning rational functions and differences

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Fang ◽  
Degui Yang ◽  
Dan Liu
Keyword(s):  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Rational Functions ◽  
Value Distribution ◽  
Exponent Of Convergence ◽  
Nonzero Constant ◽  
Zero Points

AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$ f − R , its shift $f(z+nc)$ f ( z + n c ) and the differences $\Delta _{c}^{n} f$ Δ c n f .

On the exponent of convergence of a packing of spheres

Mathematika ◽  
1966 ◽  
Vol 13 (1) ◽  
pp. 57-59 ◽  
Author(s):  
D. G. Larman
Keyword(s):  
Exponent Of Convergence

Osculatory Packings by Spheres

1970 ◽  
Vol 13 (1) ◽  
pp. 59-64 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Hausdorff Dimension ◽  
Lebesgue Measure ◽  
Simple Proof ◽  
Pairwise Disjoint ◽  
Exponent Of Convergence ◽  
Residual Set ◽  
Open Set ◽  
Finite Lebesgue Measure

If U is an open set in Euclidean N-space EN which has finite Lebesgue measure |U| then a complete packing of U by open spheres is a collection C={Sn} of pairwise disjoint open spheres contained in U and such that Σ∞n=1|Sn| = |U|. Such packings exist by Vitali's theorem. An osculatory packing is one in which the spheres Sn are chosen recursively so that from a certain point on Sn+1 is the largest possible sphere contained in (Here S- will denote the closure of a set S). We give here a simple proof of the "well-known" fact that an osculatory packing is a complete packing. Our method of proof shows also that for osculatory packings, the Hausdorff dimension of the residual set is dominated by the exponent of convergence of the radii of the Sn.

scholarly journals A further result on the complex oscillation theory of periodic second order linear differential equations

1990 ◽  
Vol 33 (1) ◽  
pp. 143-158 ◽  
Author(s):  
Shian Gao
Keyword(s):  
Entire Function ◽  
Positive Integer ◽  
Oscillation Theory ◽  
Transcendental Entire Function ◽  
Arbitrary Positive Integer ◽  
Order Of Growth ◽  
Exponent Of Convergence ◽  
Complex Oscillation ◽  
Zero Sequence ◽  
Linear Differential

We prove the following: Assume that , where p is an odd positive integer, g(ζ is a transcendental entire function with order of growth less than 1, and set A(z) = B(ezz). Then for every solution , the exponent of convergence of the zero-sequence is infinite, and, in fact, the stronger conclusion holds. We also give an example to show that if the order of growth of g(ζ) equals 1 (or, in fact, equals an arbitrary positive integer), this conclusion doesn't hold.

scholarly journals Bank-Laine Functions with Real Zeros

2020 ◽  
Vol 20 (3-4) ◽  
pp. 653-665
Author(s):  
J. K. Langley
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Explicit Representation ◽  
Trigonometric Functions ◽  
Exponent Of Convergence ◽  
Real Zeros ◽  
Real Entire Function ◽  
Bounded Below ◽  
Quasiconformal Surgery

AbstractSuppose that E is a real entire function of finite order with zeros which are all real but neither bounded above nor bounded below, such that $$E'(z) = \pm 1$$ E ′ ( z ) = ± 1 whenever $$E(z) = 0$$ E ( z ) = 0 . Then either E has an explicit representation in terms of trigonometric functions or the zeros of E have exponent of convergence at least 3. An example constructed via quasiconformal surgery demonstrates the sharpness of this result.

The exponent of convergence of poincar� series

1976 ◽  
Vol 82 (4) ◽  
pp. 297-315 ◽  
Author(s):  
S. J. Patterson
Keyword(s):  
Exponent Of Convergence
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