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Towards van der Waerden's conjecture
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Chow, Sam and Dietmann, Rainer (2023) Towards van der Waerden's conjecture. Transactions of the American Mathematical Society, 376 . pp. 2739-2785. doi:10.1090/tran/8784 ISSN 0002-9947.
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Official URL: https://doi.org/10.1090/tran/8784
Abstract
How often is a quintic polynomial solvable by radicals? We establish that the number of such polynomials, monic and irreducible with integer coefficients in [−H, H], is O(H3.91). More generally, we show that if n>3 and n /∈ {7,8,10} then there are O(Hn−1.017) monic, irreducible polynomials of degree n with integer coefficients in [−H, H]and Galois group not containing An. Save for the alternating group and degrees 7,8,10,this establishes a 1936 conjecture of van der Waerden
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Weil conjectures, Polynomials, Galois theory | |||||||||
Journal or Publication Title: | Transactions of the American Mathematical Society | |||||||||
Publisher: | American Mathematical Society | |||||||||
ISSN: | 0002-9947 | |||||||||
Official Date: | 24 January 2023 | |||||||||
Dates: |
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Volume: | 376 | |||||||||
Page Range: | pp. 2739-2785 | |||||||||
DOI: | 10.1090/tran/8784 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | First published in Transactions of the American Mathematical Society in 376, 2739-2785, 2023, published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © Copyright 2023 American Mathematical Society | |||||||||
Date of first compliant deposit: | 3 August 2022 | |||||||||
Date of first compliant Open Access: | 8 August 2022 | |||||||||
RIOXX Funder/Project Grant: |
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