The aim of this paper is to establish new transcendence criteria p-adic continued fractions. We prove that a number whose sequence partial quotients bounded in Qp and begins with arbitrarily long palindromes either quadratic or transcendental.

We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.

One goal in studying toric varieties is to put general theory in more concrete, combinatorial terms. It is striking that when one considers toric surfaces (obtained from fans in the plane) that continued fractions—an object originating in number theory—pop up in the resolution of singularities. The purpose of this article is to provide an exposition of this phenomenon and other ways in which co...

A few years ago Don Blazys caused a ripple of excitation among numerologists by presenting a real number which, applying an iterative computation recipe, produced all prime numbers. The procedure is one of an infinity of possible mappings between subsets of real numbers and subsets of integer sequences. In this particular case, the source set is that of irrational real numbers greater than 1, a...