Prime polynomials over finite fields
by Pollack, Paul, Ph.D., DARTMOUTH COLLEGE, 2008, 221 pages; 3330565

Abstract:

The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the looking glass' into the universe of polynomials. In this thesis we look at polynomial analogues of Schinzel's Hypothesis H and other problems related to the multiplicative structure of polynomial values. We obtain results both in the situation where the finite field Fq is fixed and in the more uniform situation where Fq is allowed to vary. The most important tool in these investigations is Weil's Riemann Hypothesis for global function fields, which yields an explicit form of the Chebotarev density theorem for such fields.
 
AdviserCarl Pomerance
SchoolDARTMOUTH COLLEGE
SourceDAI/B 69-10, p. , Dec 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3330565
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