COUNTING SQUAREFREE DISCRIMINANTS OF TRINOMIALS UNDER ABC

@inproceedings{Murty2009COUNTINGSD,
  title={COUNTING SQUAREFREE DISCRIMINANTS OF TRINOMIALS UNDER ABC},
  author={M. Ram Murty},
  year={2009}
}
For an odd positive integer n ≥ 5, assuming the truth of the abc conjecture, we show that for a positive proportion of pairs (a, b) of integers the trinomials of the form tn + at + b (a, b ∈ Z) are irreducible and their discriminants are squarefree. 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

On the number of real quadratic fields with class number divisible by 3

K. Chakraborty, M. Ram Murty
Proc. Amer. Math. Soc., • 2003

Exponents of class groups of quadratic fields, Topics in Number Theory (University

M. Ram Murty
Kluwer Acad. Publ., Dordrecht, • 1997
View 2 Excerpts

The Galois groups of the polynomials Xn+aXl+b

H. Osada
J. Number Theory, • 1987
View 2 Excerpts

Applications of sieve methods to the theory of numbers

C. Hooley
1976
View 2 Excerpts

The distribution of polynomials over finite fields

S. D. Cohen
Acta Arith., • 1970
View 2 Excerpts

Swinnerton-Dyer: Note on a problem of Chowla

H.P.F.B.J. Birch
Acta Arith., • 1959
View 1 Excerpt

Note on a problem of Chowla

M. Ram Murty
-1