How to explicitly solve a Thue-Mahler equation
How to generate all integral triangles containing a given angle.
Hybrid sup-norm bounds for Hecke–Maass cusp forms
Let be a Hecke–Maass cusp form of eigenvalue and square-free level . Normalize the hyperbolic measure such that and the form such that . It is shown that for all . 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
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 , 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
Hypo-Multiplicative Number - Theoretic Functions
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
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].
Identities for direct decomposability of congruences can be written in two variables
Imbrications entre le théorème de Mason, la descente de Belyi et les différentes formes de la conjecture
Soient trois éléments de l’ensemble des entiers > (resp. ) des polynômes complexes) premiers entre eux ; on note le produit des facteurs premiers (resp. le nombre des facteurs premiers dans ) du produit . La conjecture énonce que, pour tout , il existe pour lequel l’inégalité : avec max) est toujours vérifiée. Le théorème de Mason établit l’inégalité, (supposé > ) désignant le plus grand des degrés des polynômes . Les cas de triplets de polynômes où l’égalité...
Improvement on Davenport's iterative method and new results in additive number theory III
Improvement on Davenport's iterative method and new results in additive number theory, I
Improvement on Davenport's iterative method and new results in additive number theory II. Proof that G(5)≤22
In Gaussian integers has only trivial solutions – a new approach.
Incomplete exponential sums and incomplete residue systems for congruences
Indefinite quadratic forms and unipotent flows on homogeneous spaces
Indefinite Quadratic Polynomials of Small Signature.
Index form equations in quintic fields
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...
Index form equations in sextic fields: a hard computation
Inégalité de Vojta en dimension supérieure
Inequalities of DVT-type -- the one-dimensional case
In this note, particular inequalities of DVT-type in real and integer numbers are investigated.
Infinite sets of positive integers whose sums are free of powers.