Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric nÃ¤Ä±ve height on the multiplicative group of algebraic numbers. We give a non-Archimedean version of theâ€¦ (More)

In this paper, we introduce and study several norms which are constructed in order to satisfy an extremal property with respect to the Mahler measure. These norms are a natural generalization of theâ€¦ (More)

We generalize Dirichletâ€™s S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying overâ€¦ (More)

The complex process of spermatogenesis is regulated by various factors. In this study, the in vitro effects of follicle-stimulating hormone and testosterone on spermatogonial cell colony formationâ€¦ (More)

We generalize Dirichletâ€™s S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying overâ€¦ (More)