Results 11 to 20 of about 6,991,423 (313)
On exceptional sets in Manin’s conjecture [PDF]
Research in the Mathematical Sciences, 2018 In this survey paper we study Manin's Conjecture from a geometric perspective. The focus of the paper is the recent conjectural description of the exceptional set in Manin's Conjecture due to Lehmann-Sengupta-Tanimoto. After giving an extensive background, we give a precise description of this set and compute it in many examples.
Brian Lehmann, Sho Tanimoto
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Wiman's type inequality for analytic and entire functions and $h$-measure of an exceptional sets
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $\mathcal{E}_R$ be the class of analytic functions $f$ represented by power series of the form $f(z)=\sum\limits\limits_{n=0}^{+\infty}a_n z^n$ with the radius of convergence $R:=R(f)\in(0;+\infty].$ For $r\in [0, R)$ we denote the maximum modulus by
O.B. Skaskiv, A.O. Kuryliak
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Exceptional Sets for Nonuniformly Hyperbolic Diffeomorphisms [PDF]
Journal of Dynamics and Differential Equations, 2018 For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff dimension of $A$ is smaller than the Hausdorff dimension $d$ of some ergodic hyperbolic measure, then the topological ...
Sara Campos, Katrin Gelfert
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Effective uniqueness of Parry measure and exceptional sets in ergodic theory [PDF]
Monatshefte für Mathematik (Print), 2014 It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional sets arising ...
Kadyrov, Shirali
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Exceptional sets in homogeneous spaces and Hausdorff dimension [PDF]
, 2014 In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable flows in compact homogeneous spaces $X$ to show that the Hausdorff dimension of set of points that lie on trajectories
Kadyrov, Shirali
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On Exceptional Sets of the Hilbert Transform [PDF]
Real Analysis Exchange, 2017 We prove several theorems concerning the exceptional sets of Hilbert transform on the real line. In particular, it is proved that any null set is exceptional set for the Hibert transform of an indicator function. The paper also provides a real variable approach to the Kahane-Katsnelson theorem on divergence of Fourier series.
G. Karagulyan
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Relations between exceptional sets for additive problems [PDF]
, 2010 We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show,
Kawada, Koichi, Wooley, Trevor D.
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Wiman’s type inequalities without exceptional sets for random entire functions of several variables [PDF]
Математичні Студії, 2012 In the paper we {consider entire} functions $ fcolonmathbb{C}^pomathbb{C}, pgeq 2, $ defined by power series$ f(z)=f(z_1,ldots,z_p)=sum_{|n|=0}^{+infty}a_n z^n, %pgeq2, $ $z^n=z_1^{n_1}cdotldotscdot z_p^{n_p},$$n=(n_1,ldots,n_p).$ For $r=(r_1,ldots,r_p ...
A. O. Kuryliak, O. B. Skaskiv
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Exceptional Sets for Subharmonic Functions
Journal of Basic & Applied Sciences, 2015 Blanchet has shown that hypersurfaces of class C1 are removable singularities for subharmonic functions, provided the considered subharmonic functions satisfy certain assumptions. Later we showed that, in certain cases, it is sufficient that the exceptional sets are of finite (n-1)-dimensional Hausdorff measure.
J. Riihentaus
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Exceptional Sets and Fiber Products [PDF]
Foundations of Computational Mathematics, 2007 Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms.We show that fiber products promote such sets to become irreducible components, whereupon they can be found using techniques from numerical algebraic geometry for
Andrew J. Sommese, Charles W. Wampler
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