Document Type
Article
Publication Date
3-2011
Publication Title
International Journal of Number Theory
Abstract
We present the first explicitly known polynomials in Z[x] with nonsolvable Galois group and field discriminant of the form ±pA for p ≤ 7 a prime. Our main polynomial has degree 25, Galois group of the form PSL2(5)5.10, and field discriminant 569. A closely related polynomial has degree 120, Galois group of the form SL2(5)5.20, and field discriminant 5311. We completely describe 5-adic behavior, finding in particular that the root discriminant of both splitting fields is 125 · 5-1/12500 ≈ 124.984 and the class number of the latter field is divisible by 54.
Volume
7
Issue
2
First Page
289
Last Page
322
DOI
https://doi.org/10.1142/S1793042111004113
ISSN
1793-0421
Rights
©World Scientific Publishing Company
Recommended Citation
David P. Roberts. Nonsolvable polynomials with field discriminant 5a. International Journal of Number Theory 7 (2011), no. 2, 289-322.
Primo Type
Article
Comments
Preprint of an article published in International Journal of Number Theory, Volume 7, Issue 2, March 2011, Pages 289-322. https://doi.org/10.1142/S1793042111004113 ©World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijnt