An infinite series of Kronecker conjugate polynomials
Author:
Peter Müller
Journal:
Proc. Amer. Math. Soc. 125 (1997), 19331940
MSC (1991):
Primary 11C08, 11R09, 20B05; Secondary 11R32, 12E05, 12F10
MathSciNet review:
1396989
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Abstract: Let be a field of characteristic , a transcendental over , and be the absolute Galois group of . Then two nonconstant polynomials are said to be Kronecker conjugate if an element of fixes a root of if and only if it fixes a root of . If is a number field, and where is the ring of integers of , then and are Kronecker conjugate if and only if the value set equals modulo all but finitely many nonzero prime ideals of . In 1968 H. Davenport suggested the study of this latter arithmetic property. The main progress is due to M. Fried, who showed that under certain assumptions the polynomials and differ by a linear substitution. Further, he found nontrivial examples where Kronecker conjugacy holds. Until now there were only finitely many known such examples. This paper provides the first infinite series. The main part of the construction is group theoretic.
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Additional Information
Peter Müller
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email:
pfm@math.ufl.edu
DOI:
http://dx.doi.org/10.1090/S0002993997038926
PII:
S 00029939(97)038926
Received by editor(s):
January 18, 1996
Additional Notes:
The author thanks the Deutsche Forschungsgemeinschaft (DFG) for its support in form of a postdoctoral fellowship.
Communicated by:
William W. Adams
Article copyright:
© Copyright 1997 American Mathematical Society
