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Hybrid sup-norm bounds for Hecke–Maass cusp forms

Nicolas Templier (2015)

Journal of the European Mathematical Society

Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N . Normalize the hyperbolic measure such that vol ( Y 0 ( N ) ) = 1 and the form f such that ∥ f ∥ 2 = 1 . It is shown that ∥ f ∥ ∞ ≪ ϵ λ 5 24 + ϵ N 1 3 + ϵ for all ϵ > 0 . This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ k ̅ m , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ ℂ m .

Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0

Mollin, R. (2002)

Serdica Mathematical Journal

This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].

Imbrications entre le théorème de Mason, la descente de Belyi et les différentes formes de la conjecture ( a b c )

Michel Langevin (1999)

Journal de théorie des nombres de Bordeaux

Soient A , B , C = A + B trois éléments de l’ensemble ℕ * des entiers > 0 (resp. ℂ [ X ] ) des polynômes complexes) premiers entre eux ; on note r ( A B C ) le produit des facteurs premiers (resp. le nombre des facteurs premiers dans ℂ [ X ] ) du produit A B C . La conjecture ( a b c ) énonce que, pour tout ϵ > 0 , il existe C ϵ > 0 pour lequel l’inégalité : r ( A B C ) ≥ C ϵ S 1 - ϵ avec S = max ( A , B , C ) ) est toujours vérifiée. Le théorème de Mason établit l’inégalité, D (supposé > 0 ) désignant le plus grand des degrés des polynômes A , B , C : r ( A B C ) ≥ D + 1 . Les cas de triplets de polynômes où l’égalité...

Index form equations in quintic fields

István Gaál, Kálmán Győry (1999)

Acta Arithmetica

The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit...

Currently displaying 421 – 440 of 1554