Tamely Ramified Towers and Discriminant Bounds for Number Fields—II
✍ Scribed by Farshid Hajir; Christian Maire
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 245 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R 0 (2m) be the minimal root discriminant for totally complex number fields of degree 2m, and put α 0 = lim infm R 0 (2m). Define R 1 (m) to be the minimal root discriminant of totally real number fields of degree m and put α 1 = lim infm R 1 (m). Assuming the Generalized Riemann Hypothesis, α 0 ≥ 8πe γ ≈ 44.7, and, α 1 ≥ 8πe γ+π/2 ≈ 215.3. By constructing number fields of degree 12 with suitable properties, we give the best known upper estimates for α 0 and α 1 : α 0 < 82.2, α 1 < 954.3.