Effective measures for algebraic independence of the values of Mahler type functions
Effective measures of irrationality for cubic extensions of number fields
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Effective oscillation theorems for a general class of real-valued remainder terms
Effective polynomial upper bounds to perigees and numbers of (3x+d)-cycles of a given oddlength
Effective results for Diophantine equations over finitely generated domains
Let A be an arbitrary integral domain of characteristic 0 that is finitely generated over ℤ. We consider Thue equations F(x,y) = δ in x,y ∈ A, where F is a binary form with coefficients from A, and δ is a non-zero element from A, and hyper- and superelliptic equations in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and . Under the necessary finiteness conditions we give effective upper bounds for the sizes of the solutions of the equations in terms of appropriate representations for A, δ, F, f, m. These...
Effective results for linear equations in two unknowns from a multiplicative division group
Effective results for restricted rational approximation to quadratic irrationals
Effective simultaneous approximation of complex numbers by conjugate algebraic integers
We study effectively the simultaneous approximation of n-1 different complex numbers by conjugate algebraic integers of degree n over ℤ(√-1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n-1 different complex numbers lie symmetrically about the real axis, then ℤ(√-1) can be replaced by ℤ. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an idea of H....
Effective solution of families of Thue equations containing several parameters
Effective solution of the D(-1)-quadruple conjecture
Effective solution of two simultaneous Pell equations by the elliptic logarithm method
Effective version of Tartakowsky's Theorem
Effectively computable bounds for the solutions of certain diophantine equations
Effektive Konstruktion der algebraischen Erweiterungen von GF (p) sowie der vollständigen Kreisteilungskörper.
Efficient computation of addition chains
The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of operations required...
Egyptian fractions with restrictions
Eichler cohomology and periods of modular forms on p-adic Schottky groups.
Eichler Commutation Relations for Theta Series of Nebentypus.
Eigenfunctions of the laplacian, quantum chaos, and computation