Related papers: Linear forms of a given Diophantine type
We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher degree forms and relate some solutions to an unsolvable…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We describe the spectrum of ordinary Diophantine exponents for $d$-dimensional lattices. The result reduces the problem to two-dimensional case and uses argument of metric theory.
We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.
Linear forms in logarithms have an important role in the theory of Diophantine equations. In this article, we prove explicit $p$-adic lower bounds for linear forms in $p$-adic logarithms of rational numbers using Pad\'e approximations of…
We give a simple proof of a recent inequality by W.M. Schmidt and L. Summerer concerning Diophantine exponents for a linear form in three real variables.
We prove that small deformations of canonical singularities are canonical.
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…
Let R be a recursive subring of a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z].
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.
We prove a result on the structure of a Diophantine spectrum associated with Minkowski diagonal continued fraction.
In this note, finite type epimorphisms of rings are characterized.
The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong…
We prove a result on linear forms related to Peres-Schlag's theorem on badly approximable numbers with respect to lacunary sequences.
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence…
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.
In this note we collect some results on the deformation theory of toric Fano varieties.