Prime Numbers and Irreducible Polynomials

@article{Murty2002PrimeNA,
  title={Prime Numbers and Irreducible Polynomials},
  author={M. R. Murty},
  journal={The American Mathematical Monthly},
  year={2002},
  volume={109},
  pages={452 - 458}
}
  • M. R. Murty
  • Published 2002
  • Mathematics, Computer Science
  • The American Mathematical Monthly
  • The similarity between prime numbers and irreducible polynomials has been a dominant theme in the development of number theory and algebraic geometry. There are certain conjectures indicating that the connection goes well beyond analogy. For example, there is a famous conjecture of Buniakowski formulated in 1854 (see Lang [3, p. 323]), independently reformulated by Schinzel, to the effect that any irreducible polynomial f (x) in 7[x] such that the set of values f (Z+) has no common divisor… CONTINUE READING
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    References

    SHOWING 1-10 OF 12 REFERENCES
    Some Irreducible Polynomials which are Reducible mod p for all p
    • 4
    Algebra
    • 5,388
    Problems and theorems in analysis
    • 1,518
    On an irreducibility theorem of A
    • Cohn, Canadian Journal of Mathematics
    • 1981
    His monograph Nonvanishing of L-Functions and Applications , written jointly with V
    • He was a member of the Institute for Advanced Study and the Tata Institute of Fundamental Research on numerous occasions. He was E.W.R. Steacie Fellow and elected Fellow of the Royal Society of Canada
    • 1990
    His monograph Nonvanishing of L-Functions and Applications, written jointly with V. Kumar Murty and published by Birkhäuser-Verlag, won the 1996 Balaguer Prize
    • He was E.W.R. Steacie Fellow (1991-93), Killam Research Fellow
    • 1990
    Irreducibility Criteria for Polynomials with non-negative Coefficients
    • 8
    Problems and Theorems in Analysis, vol
    • 2, Springer-Verlag, New York,
    • 1976
    Filaseta and A . Odlyzko , On an irreducibility theorem of A
    • Cohn , Canadian Journal of Mathematics