The Distribution of Irreducible Polynomials in Several Indeterminates II

L. Carlitz

doi:10.4153/CJM-1965-025-1

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known that the number of normalized irreducible polynomials of degree m in a single indeterminate, with coefficients in GF(q), is given by

(1.1)

where μ(r) is the Möbius function. It follows from (1) that

(12)

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Cohen, Stephen D. 1968. The distribution of irreducible polynomials in several indeterminates over a finite field. Proceedings of the Edinburgh Mathematical Society, Vol. 16, Issue. 1, p. 1.

Cohen, Stephen D. 1969. Further Arithmetical Functions in Finite Fields. Proceedings of the Edinburgh Mathematical Society, Vol. 16, Issue. 4, p. 349.

Cohen, Stephen D. 1970. Some arithmetical functions in finite fields. Glasgow Mathematical Journal, Vol. 11, Issue. 1, p. 21.

Fredman, M. L. 1972. The distribution of absolutely irreducible polynomials in several indeterminates. Proceedings of the American Mathematical Society, Vol. 31, Issue. 2, p. 387.

1975. Abstract Analytic Number Theory. Vol. 12, Issue. , p. 297.

Knopfmacher, J 1976. Arithmetical properties of finite graphs and polynomials. Journal of Combinatorial Theory, Series B, Vol. 20, Issue. 3, p. 205.

1977. The Theory of Error-Correcting Codes. Vol. 16, Issue. , p. 703.

Wan, Daqing 1992. Zeta functions of algebraic cycles over finite fields. Manuscripta Mathematica, Vol. 74, Issue. 1, p. 413.

Jakobsen, Thomas 1998. Advances in Cryptology — CRYPTO '98. Vol. 1462, Issue. , p. 212.

2001. Number Theory Arising From Finite Fields.

Ragot, Jean-François 2002. Probabilistic absolute irreducibility test for polynomials. Journal of Pure and Applied Algebra, Vol. 172, Issue. 1, p. 87.

Panario, Daniel 2004. Finite Fields and Applications. Vol. 2948, Issue. , p. 89.

von zur Gathen, Joachim 2008. Counting reducible and singular bivariate polynomials. Finite Fields and Their Applications, Vol. 14, Issue. 4, p. 944.

Hou, Xiang-dong and Mullen, Gary L. 2009. Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields. Finite Fields and Their Applications, Vol. 15, Issue. 3, p. 304.

von zur Gathen, Joachim Viola, Alfredo and Ziegler, Konstantin 2010. LATIN 2010: Theoretical Informatics. Vol. 6034, Issue. , p. 243.

Bodin, Arnaud 2010. Generating series for irreducible polynomials over finite fields. Finite Fields and Their Applications, Vol. 16, Issue. 2, p. 116.

von zur Gathen, Joachim 2011. Counting decomposable multivariate polynomials. Applicable Algebra in Engineering, Communication and Computing, Vol. 22, Issue. 3, p. 165.

von zur Gathen, Joachim Viola, Alfredo and Ziegler, Konstantin 2013. Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields. SIAM Journal on Discrete Mathematics, Vol. 27, Issue. 2, p. 855.

von zur Gathen, Joachim and Ziegler, Konstantin 2015. Computer Algebra and Polynomials. Vol. 8942, Issue. , p. 50.

Article contents

The Distribution of Irreducible Polynomials in Several Indeterminates II

Extract

References

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The Distribution of Irreducible Polynomials in Several Indeterminates II

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests