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 -