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Results tagged with polynomials
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user 69480
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Can Davenport's estimate be extended to cubic polynomials with non-zero discriminant?
In 1961 Davenport showed that $H$ large enough there is a constant $c > 0$ such that
$$
\sum \lvert D(P) \rvert^{-1/2} < c H^2
$$
where the sum is taken over the irreducible polynomials of degree $3$ with … So, my question is: does the above estimate holds when the sum is taken over polynomials with $D(P) \neq 0$, instead of just irreducible polynomials?
[1] Davenport, H. (1961). …
