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Quantitative Hilbert Irreducibility and Almost Prime Values of Polynomial Discriminants.
- Source :
-
IMRN: International Mathematics Research Notices . Feb2023, Vol. 2023 Issue 3, p2188-2214. 27p. - Publication Year :
- 2023
-
Abstract
- We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert's Irreducibility Theorem for degree |$n$| polynomials |$f$| with |$\textrm {Gal}(f) \subseteq A_n$|. We study this both for monic polynomials and non-monic polynomials. Second, we study lower bounds on the number of degree |$n$| monic polynomials with almost prime discriminants, as well as the closely related problem of lower bounds on the number of degree |$n$| number fields with almost prime discriminants. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*ARITHMETIC
*STATISTICS
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2023
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 161877083
- Full Text :
- https://doi.org/10.1093/imrn/rnab296