Explicit formulas for strong Davenport pairs

@inproceedings{Bluher2004ExplicitFF,
  title={Explicit formulas for strong Davenport pairs},
  author={Antonia W. Bluher},
  year={2004}
}
A pair of separable polynomials (g, h) over a finite field F is said to be a strong Davenport pair if g(K) = h(K) for all finite extension fields K/F , where g(K) = { g(a) | a ∈ K }. We construct examples for which g is a projective or additive polynomial, and we find a factorization of g(x)−h(y). In addition, we prove that |g−1(a)∩K| = |h−1(a) ∩ K| for all a ∈ K. Though the existence of such examples was known to Fried, the explicit formulas for g and h are new, as are our methods of proof… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 10 REFERENCES

Cassou - Noguès et J . - M . Couveignes , Factorisations explicites de g ( y ) − h ( z )

D. J. Lewis, A. Schinzel
  • Acta Arith .
  • 1999

Couveignes, Factorisations explicites de g(y)−h(z)

P. Cassou-Noguès et J.-M
  • Acta Arith
  • 1999
VIEW 1 EXCERPT

Some unsolved problems on polynomials, in: Neki nerešeni problemi u matematici [Some Unsolved Problems in Mathematics], Matematička Biblioteka 25, Zavod za Izdavanje Udžbenika

A. Schinzel
  • Mathematics Research Group National Security Agency 9800 Savage Road,
  • 1963