Artin -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
Fix an element in a quadratic field . Define as the set of rational primes , for which has maximal order modulo . Under the assumption of the generalized Riemann hypothesis, we show that has a density. Moreover, we give necessary and sufficient conditions for the density of to be positive.
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
Let be a finite extension of , let , respectively , be the division fields of level , respectively , arising from a Lubin-Tate formal group over , and let Gal(). It is known that the valuation ring cannot be free over its associated order in unless . We determine explicitly under the hypothesis that the absolute ramification index of is sufficiently large.
Asymptotic distribution and symmetric means of algebraic numbers
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
We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure of a polynomial where is the integral of over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding , in particular as k → ∞.
Asymptotic properties of Dedekind zeta functions in families of number fields
The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for 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 .
Asymptotics of number fields and the Cohen–Lenstra heuristics
We study the asymptotics conjecture of Malle for dihedral groups of order , where 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.
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.
Automorphism groups of Ree type Deligne-Lusztig curves and function fields.
Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.