All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 98 Next

Displaying 1941 – 1960 of 1964

Showing per page

Automorphisms with exotic orbit growth

Stephan Baier, Sawian Jaidee, Shaun Stevens, Thomas Ward (2013)

Acta Arithmetica

The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism...

Automorphy for some l-adic lifts of automorphic mod l Galois representations. II

Richard Taylor (2008)

Publications Mathématiques de l'IHÉS

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.

Automorphy for some l-adic lifts of automorphic mod l Galois representations

Laurent Clozel, Michael Harris, Richard Taylor (2008)

Publications Mathématiques de l'IHÉS

We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this...

Autour de la conjecture de Zilber-Pink

Gaël Rémond (2009)

Journal de Théorie des Nombres de Bordeaux

Nous dressons un rapide panorama de résultats allant dans le sens de la conjecture suivante : l’intersection d’une sous-variété X d’une variété semi-abélienne A et de l’union de tous les sous-groupes algébriques de A de codimension au moins dim X + 1 n’est pas Zariski-dense dans X dès que X n’est pas contenue dans un sous-groupe algébrique strict de A .

Average order in cyclic groups

Joachim von zur Gathen, Arnold Knopfmacher, Florian Luca, Lutz G. Lucht, Igor E. Shparlinski (2004)

Journal de Théorie des Nombres de Bordeaux

For each natural number n we determine the average order α ( n ) of the elements in a cyclic group of order n . We show that more than half of the contribution to α ( n ) comes from the ϕ ( n ) primitive elements of order n . It is therefore of interest to study also the function β ( n ) = α ( n ) / ϕ ( n ) . We determine the mean behavior of α , β , 1 / β , and also consider these functions in the multiplicative groups of finite fields.

Average r-rank Artin conjecture

Lorenzo Menici, Cihan Pehlivan (2016)

Acta Arithmetica

Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups Γ = ⟨ a ₁ , . . . , a r ⟩ ⊂ ℚ * , with a i ∈ ℤ and a i ≤ T i , with a range of uniformity T i > e x p ( 4 ( l o g x l o g l o g x ) 1 / 2 ) for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...

Average Value of the Euler Function on Binary Palindromes

William D. Banks, Igor E. Shparlinski (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We study values of the Euler function φ(n) taken on binary palindromes of even length. In particular, if ℬ 2 ℓ denotes the set of binary palindromes with precisely 2ℓ binary digits, we derive an asymptotic formula for the average value of the Euler function on ℬ 2 ℓ .

Currently displaying 1941 – 1960 of 1964