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The polynomial analogue of a theorem of Rényi
Author(s):
Kent
E.
Morrison
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2897-2902.
MSC (2000):
Primary 11T06;
Secondary 11T55, 05A16
Posted:
April 25, 2005
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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.
References:
-
- 1.
- L. Carlitz. An application of a theorem of Stickelberger, Simon Stevin 31 (1956) 27-30. MR 0080696 (18:285g)
- 2.
- L. Gegenbauer. Asymptotische Gesetze der Zahlentheorie, Denkshcriften Akad. Wien 49 (1885) 37-80.
- 3.
- G. A. Jones.
 , Mathematics Magazine 66 (1993) 290-298. MR 1251442 (94m:11002) - 4.
- M. Kac. Statistical Independence in Probability, Analysis and Number Theory. Carus Monographs, no. 12. Mathematical Association of America, Washington, D.C., 1959. MR 0110114 (22:996)
- 5.
- B. Poonen. Squarefree values of multivariable polynomials, Duke Math. J. 118 (2003), no. 2, 353-373. MR 1980998 (2004d:11094)
- 6.
- K. Ramsay. Square-free values of polynomials in one variable over function fields, Internat. Math. Res. Notices, no. 4 (1992) 97-102. MR 1159451 (93b:11115)
- 7.
- A. Rényi. On the density of certain sequences of integers, Acad. Serbe Sci. Publ. Inst. Math. 8 (1955), 157-162. MR 0076787 (17,944f)
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Additional Information:
Kent
E.
Morrison
Affiliation:
Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email:
kmorriso@calpoly.edu
DOI:
10.1090/S0002-9939-05-08071-8
PII:
S 0002-9939(05)08071-8
Received by editor(s):
June 9, 2004
Posted:
April 25, 2005
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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