Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Irregularities in the distribution of irreducible polynomials
HTML articles powered by AMS MathViewer

by Kevin S. McCurley PDF
Proc. Amer. Math. Soc. 117 (1993), 11-16 Request permission

Abstract:

We prove that there exist monic polynomials $f$ over $\operatorname {GF} (q)$ for which $f + g$ is reducible for all $g \in \operatorname {GF} (q)[x]$ with small degree. This is the analogue for polynomials of a result of Erdös and Rankin concerning gaps between consecutive primes.
References
  • E. Artin, Quadratische Körper im Gebiete der höheren Kongruenzen. I, Math. Z. 19 (1924), no. 1, 153–206 (German). MR 1544651, DOI 10.1007/BF01181074
  • Don Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE Trans. Inform. Theory 30 (1984), no. 4, 587–594. MR 755785, DOI 10.1109/TIT.1984.1056941
  • William Feller, An introduction to probability theory and its applications. Vol. I, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
  • Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
    • Renet Lovorn, Ph.D. Dissertation, Dept. of Math., Univ. of Georgia, in preparation.
  • A. M. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Advances in cryptology (Paris, 1984) Lecture Notes in Comput. Sci., vol. 209, Springer, Berlin, 1985, pp. 224–314. MR 825593, DOI 10.1007/3-540-39757-4_{2}0
    • R. A. Rankin, The difference between consecutive prime numbers, Proc. London Math. Soc. 13 (1938), 242-247.
  • Georges Rhin, Répartition modulo $1$ dans un corps de séries formelles sur un corps fini, Dissertationes Math. (Rozprawy Mat.) 95 (1972), 75 (French). MR 349612
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11T06
  • Retrieve articles in all journals with MSC: 11T06
Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 11-16
  • MSC: Primary 11T06
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1107923-5
  • MathSciNet review: 1107923