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- W2952805591 abstract "A. Mukhopadhyay, M. R. Murty and K. Srinivas (this http URL) have recently studied various arithmetic properties of the discriminant $Delta_n(a,b)$ of the trinomial $f_{n,a,b}(t) = t^n + at + b$, where $n ge 5$ is a fixed integer. In particular, it is shown that, under the $abc$-conjecture, for every $n equiv 1 pmod 4$, the quadratic fields $Q(sqrt{Delta_n(a,b)})$ are pairwise distinct for a positive proportion of such discriminants with integers $a$ and $b$ such that $f_{n,a,b}$ is irreducible over $Q$ and $|Delta_n(a,b)|le X$, as $Xto infty$. We use the square-sieve and bounds of character sums to obtain a weaker but unconditional version of this result." @default.
- W2952805591 created "2019-06-27" @default.
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- W2952805591 date "2008-11-08" @default.
- W2952805591 modified "2023-09-27" @default.
- W2952805591 title "On Quadratic Fields Generated by Discriminants of Irreducible Trinomials" @default.
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