Laura Capuano

p-adically convergent loci in varieties arising from periodic continued fractions

Abstract Inspired by the existence of multiple alternative definitions of continued fraction expansions for elements in $$\mathbb {Q}_p$$ Q p , we study the p -adic convergence of periodic continued fractions with partial quotients in $$\mathbb {Z}[1/p]$$ Z [ 1 / p ] from a geome...

If a machine did it, it is probably transcendental (even p-adically)

Abstract Continued fraction expansions provide a well-established bridge between algebraic properties of numbers and combinatorics on words. In this article, we investigate the algebraicity of p -adic numbers whose continued fractions arise from certain classes of words which gen...