Sets of exact approximation order by rational numbers III
Simultaneous approximation of zero by values of integral polynomials with respect to different valuations
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations
We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve with respect to the different valuations. It is an extension of the author’s earlier results.
Slowly growing sequences and discrepancy modulo one
Some algebraic and homological properties of Lipschitz algebras and their second duals
Let be a metric space and . We study homological properties and different types of amenability of Lipschitz algebras and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of . Finally, some results concerning the character...
Systems of linear forms and covers for star bodies