TY - CHAP
T1 - Explicit hilbert’s irreducibility theorem in function fields
AU - Bary-Soroker, Lior
AU - Entin, Alexei
N1 - Publisher Copyright:
© 2021 American Mathematical Society.
PY - 2021
Y1 - 2021
N2 - We prove a quantitative version of Hilbert’s irreducibility theorem for function fields: If f (T1, . . ., Tn, X) is an irreducible polynomial over the field of rational functions in u over a finite field with q elements, then the proportion of n-tuples (t1, . . ., tn ) of monic polynomials in u of degree d for which f (t1, . . ., tn, X) is reducible out of all n-tuples of degree d monic polynomials is O(dq−d/2 ).
AB - We prove a quantitative version of Hilbert’s irreducibility theorem for function fields: If f (T1, . . ., Tn, X) is an irreducible polynomial over the field of rational functions in u over a finite field with q elements, then the proportion of n-tuples (t1, . . ., tn ) of monic polynomials in u of degree d for which f (t1, . . ., tn, X) is reducible out of all n-tuples of degree d monic polynomials is O(dq−d/2 ).
UR - http://www.scopus.com/inward/record.url?scp=85107316854&partnerID=8YFLogxK
U2 - 10.1090/conm/767/15402
DO - 10.1090/conm/767/15402
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AN - SCOPUS:85107316854
SN - 978-1-4704-5207-0
T3 - Contemporary Mathematics
SP - 125
EP - 134
BT - Abelian Varieties and Number Theory
A2 - Jarden, Moshe
A2 - Shaska, Tony
PB - American Mathematical Society
ER -