TY - JOUR
T1 - On quadratic fields generated by polynomials
AU - Luca, Florian
AU - Shparlinski, Igor E.
PY - 2008/11
Y1 - 2008/11
N2 - 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} .
AB - 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} .
UR - http://www.scopus.com/inward/record.url?scp=57349157823&partnerID=8YFLogxK
U2 - 10.1007/s00013-008-2656-2
DO - 10.1007/s00013-008-2656-2
M3 - Article
AN - SCOPUS:57349157823
SN - 0003-889X
VL - 91
SP - 399
EP - 408
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 5
ER -