Explicit hilbert’s irreducibility theorem in function fields

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 ).

Original languageEnglish
Title of host publicationAbelian Varieties and Number Theory
EditorsMoshe Jarden, Tony Shaska
PublisherAmerican Mathematical Society
Number of pages10
ISBN (Electronic)978-1-4704-6423-3
ISBN (Print)978-1-4704-5207-0
StatePublished - 2021

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


FundersFunder number
Israel Science Foundation2507/19


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