Double series over a non-Archimedean field

2014/03/13 by Luigi Corgnier, Corgnier, Luigi, Carla Massaza +3
Mathematics · #12J15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:12J15

paper · pdf · doi:10.48550/arxiv.1403.3623

arxiv created 2014/03/13 · arxiv updated 2014/03/17

Abstract

In the present paper we investigate the convergence of a double series over a complete non-Archimedean field and prove that, while the proofs are somewhat different, the Archimedean results hold true.

Related

• The intermediate value theorem over a non-Archimedean field via Hensel's Lemma
• Non-Archimedean second main theorem sharing small functions
• Basic Non-Archimedean Jørgensen Theory
• Non-Linearizability of power series over complete non-Archimedean fields of positive characteristic
• Hyperseries in the non-Archimedean ring of Colombeau generalized numbers