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Algebraic Numbers and Topologically Equivalent Measures

Description: A set-theoretical point of view to study algebraic numbers has been introduced. We extend a result of Navarro-Bermudez concerning shift invariant measures in the Cantor space which are topologically equivalent to shift invariant measures which correspond to some algebraic integers. It is known that any transcendental numbers and rational numbers in the unit interval are not binomial. We proved that there are algebraic numbers of degree greater than two so that they are binomial numbers. Algebraic integers of degree 2 are proved not to be binomial numbers. A few compositive relations having to do with algebraic numbers on the unit interval have been studied; for instance, rationally related, integrally related, binomially related, B1-related relations. A formula between binomial numbers and binomial coefficients has been stated. A generalized algebraic equation related to topologically equivalent measures has also been stated.
Date: December 1983
Creator: Huang, Kuoduo
Partner: UNT Libraries

Almost Holomorphic Poincaré Series Corresponding to Products of Harmonic Siegel–Maass Forms

Description: This article investigates Poincaré series, particularly the study of Siegel–Poincaré series of degree 2 attached to products of terms of Fourier series of harmonic Siegel–Maass forms and holomorphic Siegel modular forms
Date: April 15, 2016
Creator: Bringmann, Kathrin; Richter, Olav K. & Westerholt-Raum, Martin
Partner: UNT College of Arts and Sciences

Badly approximable points on self-affine sponges and the lower Assouad dimension

Description: This article highlights a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. The results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as Bedford–McMullen sponges/carpets) and the case of Barański carpets.
Date: June 20, 2017
Creator: Das, Tushar; Fishman, Lior; Simmons, David & Urbański, Mariusz
Partner: UNT College of Arts and Sciences