On the tacnodes of configurations of conics in the projective plane.
We obtain an estimate on the average cardinality (d,s,a) of the value set of any family of monic polynomials in of degree d for which s consecutive coefficients are fixed. Our estimate asserts that , where . We also prove that , where ₂(d,s,a) is the average second moment of the value set cardinalities for any family of monic polynomials of of degree d with s consecutive coefficients fixed as above. Finally, we show that , where ₂(d,0) denotes the average second moment for all monic polynomials...