Displaying similar documents to “A note on the limit points associated withthe generalized abc-conjecture for ℤ[t]”

A consequence of an effective form of the abc-conjecture

Jerzy Browkin (1999)

Colloquium Mathematicae


T. Cochrane and R. E. Dressler [CD] proved that the abc-conjecture implies that, for every > 0, the gap between two consecutive numbers A A 0 . 4 with two exceptions given in Table 2.

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux


Thomas’ conjecture is, given monic polynomials p 1 , ... , p d [ a ] with 0 < deg p 1 < < deg p d , then the Thue equation (over the rational integers) ( X - p 1 ( a ) Y ) ( X - p d ( a ) Y ) + Y d = 1 has only trivial solutions, provided a a 0 with effective computable a 0 . We consider a function field analogue of Thomas’ conjecture in case of degree d = 3 . Moreover we find a counterexample to Thomas’ conjecture for d = 3 .

On Garcia numbers.

Brunotte, Horst (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]


A geometric approach to the Jacobian Conjecture in ℂ²

Ludwik M. Drużkowski (1991)

Annales Polonici Mathematici


We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set g - 1 ( 0 ) (resp. f - 1 ( 0 ) ), then (f,g) is bijective.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici


We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of n . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.