@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",

}