TY - JOUR
T1 - Irreducible polynomials of bounded height
AU - Bary-Soroker, Lior
AU - Kozma, Gady
N1 - Publisher Copyright:
© 2020.
PY - 2020
Y1 - 2020
N2 - The goal of this paper is to prove that a random polynomial with independent and identically distributed random coefficients taking values uniformly in {1;::: ; 210} is irreducible with probability tending to 1 as the degree tends to infinity. Moreover, we prove that the Galois group of the random polynomial contains the alternating group, again with probability tending to 1.
AB - The goal of this paper is to prove that a random polynomial with independent and identically distributed random coefficients taking values uniformly in {1;::: ; 210} is irreducible with probability tending to 1 as the degree tends to infinity. Moreover, we prove that the Galois group of the random polynomial contains the alternating group, again with probability tending to 1.
UR - http://www.scopus.com/inward/record.url?scp=85094742986&partnerID=8YFLogxK
U2 - 10.1215/00127094-2019-0047
DO - 10.1215/00127094-2019-0047
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AN - SCOPUS:85094742986
SN - 0012-7094
VL - 169
SP - 579
EP - 598
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 4
ER -