On the maximal unramified pro-2-extension of ℤ₂-extensions of certain real quadratic fields II
On the maximal unramified pro-2-extension over the cyclotomic -extension of an imaginary quadratic field
For the cyclotomic -extension of an imaginary quadratic field , we consider the Galois group of the maximal unramified pro--extension over . In this paper, we give some families of for which is a metabelian pro--group with the explicit presentation, and determine the case that becomes a nonabelian metacyclic pro--group. We also calculate Iwasawa theoretically the Galois groups of -class field towers of certain cyclotomic -extensions.
On the maximum modulus of cyclotomic integers
On the meromorphic continuation of degree two -functions.
On the minimum of the unit lattice
On the multiplicative independence of binomial coefficients
On the -torsion subgroup of the Brauer group of a number field
Given a number field Galois over the rational field , and a positive integer prime to the class number of , there exists an abelian extension (of exponent ) such that the -torsion subgroup of the Brauer group of is equal to the relative Brauer group of .
On the Néron model of jacobians of Shimura curves
On the nonessential discriminant divisor of an algebraic number field
On the non-existence of abelian conditions governing solvability of the - 1 Pell equation.
On the non-torsion elements in the algebraic K-theory of rings of integers.
On the non-triviality of the basic Iwasawa λ-invariant for an infinitude of imaginary quadratic fields
On the number of ideals free from large prime divisors.
On the Number of Integral Ideals in Galois Extensions.
On the number of irreducible factors of a polynomial II
On the number of polynomials of bounded measure
On the number of rational points of Jacobians over finite fields
We prove lower and upper bounds for the class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta functions.
On the number of representations of a positive integer by a binary quadratic form
On the number of representations of n by ax² + bxy + cy²
On the number of sign changes in the remainder-term of the prime-ideal theorem