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Title:  Some Extensions of the SkolemMahlerLech Theorem 
Author(s):  Laohakosol, Vichian 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  The SkolemMahlerLech theorem states that if the Taylor series expansion (about the origin) of a rational function has infinitely many zero coefficients, then the set of indices of these zero coefficients forms a finite union of arithmetic progressions modulo a finite set. Since rational functions satisfy linear differential equations of order 0 with polynomial coefficients, it is natural to conjecture that the SkolemMahlerLech theorem also holds for functions satisfying linear differential equations with polynomial coefficients of higher orders. In this thesis, we treat the case of first order differential equations. We are able to answer affirmatively parts of this conjecture, for example, we are able to show that functions satisfying first order linear homogeneous differential equations with polynomial coefficients of Fuchsian type are skomal. We also extend the SkolemMahlerLech theorem in some other directions from the case of rational functions, and obtain certain arithmetical properties for functions satisfying linear differential equations with polynomial coefficients. 
Issue Date:  1983 
Type:  Text 
Description:  97 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1983. 
URI:  http://hdl.handle.net/2142/71216 
Other Identifier(s):  (UMI)AAI8409980 
Date Available in IDEALS:  20141216 
Date Deposited:  1983 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois