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- W3099110628 abstract "We study the compositum k [d] of all degree d extensions of a number field k in a fixed algebraic closure. We show k [d] contains all subextensions of degree less than d if and only if d≤4. We prove that for d>2 there is no bound c=c(d) on the degree of elements required to generate finite subextensions of k [d] /k. Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of d, but that one can take c=d when d is prime. This question was inspired by work of Bombieri and Zannier on heights in similar extensions, and previously considered by Checcoli." @default.
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- W3099110628 date "2014-01-01" @default.
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- W3099110628 title "On the compositum of all degree d extensions of a number field" @default.
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- W3099110628 doi "https://doi.org/10.5802/jtnb.884" @default.
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