Infinite class field towers of number fields of prime power discriminant
نویسندگان
چکیده
منابع مشابه
Infinite Hilbert Class Field Towers over Cyclotomic Fields
Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
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The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R2m be the minimal root discriminant for totally complex number fields of degree 2m, and put α0 = lim infmR2m. One knows that α0 ≥ 4πeγ ≈ 22.3, and, assuming the Generalized Riemann Hypothesis, α0 ≥ 8πeγ ≈ 44.7. It is of great interest to know if the latter bound is sharp. In 1978,...
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The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R0(2m) be the minimal root discriminant for totally complex number fields of degree 2m, and put α0 = lim infmR0(2m). Define R1(m) to be the minimal root discriminant of totally real number fields of degree m and put α1 = lim infmR1(m). Assuming the Generalized Riemann Hypothesis, α...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2020
ISSN: 0001-8708
DOI: 10.1016/j.aim.2020.107318