3 papers
math.NT2025
The Diophantine problem for addition and divisibility for rings of -integers of quadratic imaginary extensions of
Natalia Hormazábal, Carlos Martínez-Ranero
Let be a quadratic imaginary extension of , let be a finite nonempty set of non archimedean places, and let denote the ring of -integers…
math.LO2024
Undecidability of infinite towers of Kummer extensions of
Carlos Martinez-Ranero, Javier Utreras
We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combine…
math.GN2022
Autohomeomorphisms of the finite powers of the double arrow
Sebastian Barria, Carlos Martinez-Ranero
Let and denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that any homeomorphism is l…