Resumen de Liouville numbers in the non-archimedean case

Tuangrat Chaichana, Takao Komatsu, Vichian Laohakosol

• Basic results about real Liouville numbers are investigated in three non-archimedean settings, referred to as the non-archimedean case, comprising the ¯eld of p-adic num- bers, the function ¯eld completed with respect to the degree valuation and the function ¯eld completed with respect to a prime-adic valuation. The result of Erd}os that every real number is representable as a sum, and as a product of two real Liouville numbers is shown to hold in the non-archimedean case. The concept of Liouville continued fractions is also considered.