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We give examples of Cantor sets in of Hausdorff dimension 1 whose polynomial hulls have non-empty interior.
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We consider Cantor sets C
X,p
constructed by means of a sequence {X
k
–p
}
k=1
of random variables. We find sufficient conditions for the inequality
to hold. 相似文献
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In this paper, two types of general sets determined by partial quotients of continued fractions over the field of formal Laurent series with coefficients from a given finite field are studied. The Hausdorff dimensions of and are determined completely, where An(x) denotes the partial quotients in the continued fraction expansion (in case of Laurent series) of x and (n) is a positive valued function defined on natural numbers N. 相似文献
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Luming Shen Chao Ma Yuehua Liu 《分析论及其应用》2007,23(2):171-179
For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈(0,1]:1〈dj(x)/h(j-1)(d(j-1)(x))≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number. 相似文献
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We establish an asymptotic formula with a power savings in the error term for traces of CM values of a family of Maass–Poincaré series which contains the modular j-function as a special case. By work of Borcherds (1998) [2], Zagier (2002) [31], and Bringmann and Ono (2007) [4], these traces are Fourier coefficients of half-integral weight weakly holomorphic modular forms and Maass forms. 相似文献