The polynomial analogue of a theorem of Rényi
Author:
Kent E. Morrison
Journal:
Proc. Amer. Math. Soc. 133 (2005), 2897-2902
MSC (2000):
Primary 11T06; Secondary 11T55, 05A16
DOI:
https://doi.org/10.1090/S0002-9939-05-08071-8
Published electronically:
April 25, 2005
MathSciNet review:
2159767
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Rényi's result on the density of integers whose prime factorizations have excess multiplicity has an analogue for polynomials over a finite field.
- 1. L. Carlitz, An application of a theorem of Stickelberger, Simon Stevin 31 (1956), 27–30. MR 0080696
- 2. L. Gegenbauer. Asymptotische Gesetze der Zahlentheorie, Denkshcriften Akad. Wien 49 (1885) 37-80.
- 3. Gareth A. Jones, 6/𝜋², Math. Mag. 66 (1993), no. 5, 290–298. MR 1251442, https://doi.org/10.2307/2690503
- 4. Mark Kac, Statistical independence in probability, analysis and number theory., The Carus Mathematical Monographs, No. 12, Published by the Mathematical Association of America. Distributed by John Wiley and Sons, Inc., New York, 1959. MR 0110114
- 5. Bjorn Poonen, Squarefree values of multivariable polynomials, Duke Math. J. 118 (2003), no. 2, 353–373. MR 1980998, https://doi.org/10.1215/S0012-7094-03-11826-8
- 6. Keith Ramsay, Square-free values of polynomials in one variable over function fields, Internat. Math. Res. Notices 4 (1992), 97–102. MR 1159451, https://doi.org/10.1155/S1073792892000114
- 7. Alfred Rényi, On the density of certain sequences of integers, Acad. Serbe Sci. Publ. Inst. Math. 8 (1955), 157–162. MR 0076787
, Mathematics Magazine 66 (1993) 290-298. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11T06, 11T55, 05A16
Retrieve articles in all journals with MSC (2000): 11T06, 11T55, 05A16
Additional Information
Kent E. Morrison
Affiliation:
Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email:
kmorriso@calpoly.edu
DOI:
https://doi.org/10.1090/S0002-9939-05-08071-8
Received by editor(s):
June 9, 2004
Published electronically:
April 25, 2005
Communicated by:
David E. Rohrlich
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.