On quadratic fields generated by polynomials

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Let f(X) ε ℤ [X] be a polynomial of degree d ≥ 2 without multiple roots. Under the assumption of the ABC-conjecture, an asymptotic formula for the number of distinct fields among ℚ(√f(n) ) for n ε {1,...,N} has recently been given by Cutter, Granville, and Tucker. We use bounds for character sums to obtain an unconditional lower bound on the number of such fields for n ε {M + 1,..., M + N} .

Original languageEnglish
Pages (from-to)399-408
Number of pages10
JournalArchiv der Mathematik
Issue number5
Publication statusPublished - Nov 2008

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