@inbook{8219bbc2ebd14998b2a06710bcf93a64,
title = "Explicit hilbert{\textquoteright}s irreducibility theorem in function fields",
abstract = "We prove a quantitative version of Hilbert{\textquoteright}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 ).",
author = "Lior Bary-Soroker and Alexei Entin",
note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",
year = "2021",
doi = "10.1090/conm/767/15402",
language = "אנגלית",
isbn = "978-1-4704-5207-0",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "125--134",
editor = "Moshe Jarden and Tony Shaska",
booktitle = "Abelian Varieties and Number Theory",
address = "ארצות הברית",
}