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Fix an element $α$ in a quadratic field $K$ . Define $S$ as the set of rational primes $p$ , for which $α$ has maximal order modulo $p$ . Under the assumption of the generalized Riemann hypothesis, we show that $S$ has a density. Moreover, we give necessary and sufficient conditions for the density of $S$ to be positive.

Aspects numériques de la détermination du l-groupe des classes d'idéaux des extensions cycliques de degré premier l

Georges Gras (1972/1973)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Associated orders of certain extensions arising from Lubin-Tate formal groups

Nigel P. Byott (1997)

Journal de théorie des nombres de Bordeaux

Let $k$ be a finite extension of $ℚ_{p}$ , let $k_{1}$ , respectively $k_{3}$ , be the division fields of level $1$ , respectively $3$ , arising from a Lubin-Tate formal group over $k$ , and let $Γ =$ Gal( $k_{3} / k_{1}$ ). It is known that the valuation ring $k_{3}$ cannot be free over its associated order $𝔄$ in $K Γ$ unless $k = ℚ_{p}$ . We determine explicitly under the hypothesis that the absolute ramification index of $k$ is sufficiently large.

Asymptotic distribution and symmetric means of algebraic numbers

Igor E. Pritsker (2015)

Acta Arithmetica

Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the...

Asymptotic nature of higher Mahler measure

(2014)

Acta Arithmetica

We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure $m_{k} (P)$ of a polynomial $P,$ where $m_{k} (P)$ is the integral of $l o g^{k} | P |$ over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding $m_{k} (P)$ , in particular $| m_{k} (P) | / k! \to 1 / π$ as k → ∞.

Asymptotic properties of Dedekind zeta functions in families of number fields

Alexey Zykin (2010)

Journal de Théorie des Nombres de Bordeaux

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $ℜ s > 1 / 2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer–Siegel theorem. As an application we obtain a limit formula for Euler–Kronecker constants in families of number fields.

Asymptotically exact heuristics for prime divisors of the sequence ${a^{k} + b^{k}}_{k = 1}^{\infty}$ .

Moree, Pieter (2006)

Journal of Integer Sequences [electronic only]

Asymptotics of number fields and the Cohen–Lenstra heuristics

Jürgen Klüners (2006)

Journal de Théorie des Nombres de Bordeaux

We study the asymptotics conjecture of Malle for dihedral groups $D_{ℓ}$ of order $2 ℓ$ , where $ℓ$ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen–Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

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Displaying 361 – 380 of 3416

Arten und Gattungen von Abbildungsgruppen. Ein elementares Beispiel aus der Galoisschen Theorie.

Artin formalism and heat kernels.

Artin $L$ -functions and normalization of intertwining operators

Artin L-functions and modular forms associated to quasi-cyclotomic fields

Artin-Root Numbers and Normal Integral Bases for Quaternion Fields.

Artin's conjecture in algebraic number fields and a related question concerning units

Artin's conjecture on primes with prescribed primitive roots

Artin's primitive root conjecture for quadratic fields

Aspects numériques de la détermination du l-groupe des classes d'idéaux des extensions cycliques de degré premier l

Associated orders of certain extensions arising from Lubin-Tate formal groups

Asymptotic distribution and symmetric means of algebraic numbers

Asymptotic nature of higher Mahler measure

Asymptotic properties of Dedekind zeta functions in families of number fields

Asymptotically exact heuristics for prime divisors of the sequence ${a^{k} + b^{k}}_{k = 1}^{\infty}$ .

Asymptotics of number fields and the Cohen–Lenstra heuristics

Atkin-Lehner involutions and class number residuality

Au sujet de l'algorithme « de Coates »

Automorphic vector bundles on connected Shimura varieties.

Automorphism Groups of Algebraic Function Fields.

Automorphism Groups of Algebraic Number Fields.

Currently displaying 361 – 380 of 3416