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The probability
of relatively prime polynomials in $\mathbb{Z}_{p^k}[x]$
Thomas R. Hagedorn and Jeffrey Hatley
Vol. 3 (2010), No. 2, 223–232
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Abstract |
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Let denote the probability that two randomly chosen monic polynomials , of degrees and , respectively, are relatively prime. Let be a prime power. We establish an explicit formula for when , the ring of integers mod . |
Keywords
relatively prime polynomials
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Mathematical Subject Classification 2000
Primary: 11C20, 13B25, 13F20
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Milestones
Received: 11 December 2009
Revised: 25 April 2010
Accepted: 26 April 2010
Published: 11 August 2010
Communicated by Arthur T. Benjamin
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Authors |
| Thomas R. Hagedorn | |
| The College of New Jersey Department of Mathematics and Statistics P.O. Box 7718 Ewing, NJ 08628 United States |
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| Jeffrey Hatley | |
| The College of New Jersey Department of Mathematics and Statistics P.O. Box 7718 Ewing, NJ 08628 United States |
Department of Mathematics and
Statistics University of Massachusetts at Amherst Amherst, MA 01003 |
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