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Displaying 61 – 80 of 267

The distribution of polynomials over finite fields, II

Stephen Cohen (1972)

Acta Arithmetica

The distribution of powers of integers in algebraic number fields

Werner Georg Nowak, Johannes Schoißengeier (2004)

Journal de Théorie des Nombres de Bordeaux

For an arbitrary (not totally real) number field $K$ of degree $\geq 3$ , we ask how many perfect powers $γ^{p}$ of algebraic integers $γ$ in $K$ exist, such that $μ (τ (γ^{p})) \leq X$ for each embedding $τ$ of $K$ into the complex field. ( $X$ a large real parameter, $p \geq 2$ a fixed integer, and $μ (z) = max (| Re (z) |, | Im (z) |)$ for any complex $z$ .) This quantity is evaluated asymptotically in the form $c_{p, K} X^{n / p} + R_{p, K} (X)$ , with sharp estimates for the remainder $R_{p, K} (X)$ . The argument uses techniques from lattice point theory along with W. Schmidt’s multivariate extension of K.F. Roth’s result on the approximation...

The distribution of second $p$ -class groups on coclass graphs

Daniel C. Mayer (2013)

Journal de Théorie des Nombres de Bordeaux

General concepts and strategies are developed for identifying the isomorphism type of the second $p$ -class group $G = Gal (F_{p}^{2} (K) | K)$ , that is the Galois group of the second Hilbert $p$ -class field $F_{p}^{2} (K)$ , of a number field $K$ , for a prime $p$ . The isomorphism type determines the position of $G$ on one of the coclass graphs $𝒢 (p, r)$ , $r \geq 0$ , in the sense of Eick, Leedham-Green, and Newman. It is shown that, for special types of the base field $K$ and of its $p$ -class group ${Cl}_{p} (K)$ , the position of $G$ is restricted to certain admissible branches of coclass...

Currently displaying 61 – 80 of 267

Previous Page 4 Next

Displaying 61 – 80 of 267

The distribution of polynomials over finite fields, II

The distribution of powers of integers in algebraic number fields

The distribution of second $p$ -class groups on coclass graphs

The distribution of the fundamental units of real quadratic fields

The distribution of zeros of Epstein zeta functions over GLₙ

The Divisibility of Normal Integral Generators.

The Elementary Theory of Algebraic Fields of Finite Corank.

The EM Algorithm applied to determining new limit points of Mahler measures

The equation xyz = x + y + z = 1 in integers of a cubic field.

The equation xyz=x+y+z=1 in integers of a quartic field

The Erdős Theorem and the Halberstam Theorem in function fields

The Euclidean algorithm for Galois extensions of Q.

The existence of certain infinite families of imaginary quadratic fields.

The explicit Hilbert 2-cyclic class field for Q (... -p).

The exponent of class groups on congruence function fields

The factorization of an integral matrix into a product of two integral symmetric matrices I

The factorization of certain quadrinominals.

The Fekete-Szegő theorem with splitting conditions: Part I

The Fekete-Szegő theorem with splitting conditions: Part II

The field descent and class groups of CM-fields

Currently displaying 61 – 80 of 267