Cover Image

The Diophantine problem for addition and divisibility for rings of $S$-integers of quadratic imaginary extensions of $\mathbb{Q}$

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Hormazábal, Natalia, Martínez-Ranero, Carlos
Format:	Preprint
Published:	2025
Subjects:	Number Theory Logic Primary: 11U05, Secondary: 03B25
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Diophantine Maps
by: Eggink, A.
Published: (2024)

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence
by: Khani, Mohsen, et al.
Published: (2021)

Undecidability of infinite towers of Kummer extensions of $\mathbb{F}_p(t)$
by: Martinez-Ranero, Carlos, et al.
Published: (2024)

Mixed quantifier prefixes over Diophantine equations with integer variables
by: Sun, Zhi-Wei
Published: (2021)

Undecidability of expansions of Laurent series fields by cyclic discrete subgroups
by: Gitin, Leo
Published: (2024)

Hilbert's tenth problem for rings of holomorphic functions of bounded order
by: Pasten, Hector
Published: (2024)

Undecidability of infinite algebraic extensions of $\mathbb{F}_p(t)$
by: Martinez-Ranero, Carlos, et al.
Published: (2024)

Undecidability on Diophantine equations over $\mathbb Z[i]$ with $20$ unknowns
by: Matiyasevich, Yuri, et al.
Published: (2025)

Considering The Satisfiability of Cubic Diophantine Equations
by: Rosko, Milan
Published: (2025)

Decidability of polynomial equations over function fields in positive characteristic
by: Daans, Nicolas
Published: (2025)

First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability
by: Shlapentokh, Alexandra, et al.
Published: (2024)

Definability and decidability for rings of integers in totally imaginary fields
by: Springer, Caleb
Published: (2022)

On the Diophantine problem related to power circuits
by: Rybalov, Alexander
Published: (2025)

Decidability of Extensions of Presburger Arithmetic by Hardy Field Functions
by: Brown, Hera, et al.
Published: (2025)

Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers
by: Daans, Nicolas
Published: (2023)

New consequences of PFA($T^*$)
by: Martínez-Ranero, Carlos, et al.
Published: (2025)

Distal expansions of Presburger arithmetic by a sparse predicate
by: Tong, Mervyn
Published: (2024)

Integer-valued o-minimal functions
by: Bhardwaj, Neer, et al.
Published: (2024)

Monochromatic sums and quotients in $\mathbb N$
by: Di Nasso, Mauro, et al.
Published: (2026)

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field
by: Alpöge, Levent, et al.
Published: (2025)

Hilbert's tenth problem for families of $ \mathbb{Z}_p $-extensions of imaginary quadratic fields
by: Müller, Katharina, et al.
Published: (2024)

Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
by: Khani, Mohsen, et al.
Published: (2025)

Ultracontact algebras and stack systems
by: Carai, Luca, et al.
Published: (2026)

Algorithms for Modular Parametrizations of Elliptic Curves over $\mathbb{Q}$
by: Wang, SanMin
Published: (2025)

First-order definability of Darmon points in number fields
by: De Rasis, Juan Pablo, et al.
Published: (2024)

A note on the theory of well orders
by: Jeřábek, Emil
Published: (2024)

Defining $\mathbb Z$ using unit groups
by: Mazur, Barry, et al.
Published: (2023)

Lang-Weil Type Estimates in Finite Difference Fields
by: Hils, Martin, et al.
Published: (2024)

A choice-free proof of Mal'cev's theorem on quasivarieties
by: Shen, Guozhen
Published: (2025)

Three forms of the Erdős-Dushnik-Miller Theorem
by: Howard, Paul, et al.
Published: (2024)

Hilbert's Tenth Problem for some Noncommutative Rings
by: Eggink, A.
Published: (2024)

An ordinal analysis of CM and its extensions
by: Wang, Shuwei
Published: (2025)

Towards a theory of symmetric extensions
by: Karagila, Asaf, et al.
Published: (2026)

Upwards homogeneity in iterated symmetric extensions
by: Ryan-Smith, Calliope, et al.
Published: (2024)

On the tower factorization of integers
by: De Koninck, Jean-Marie, et al.
Published: (2023)

On the theory of exponential integer parts
by: Jeřábek, Emil
Published: (2024)

Path of pathology
by: Filipów, Rafał, et al.
Published: (2024)

Partition regularity in imaginary quadratic rings of integers
by: Donoso, Sebastián, et al.
Published: (2026)

Exponential sums and motivic oscillation index of arbitrary ideals and their applications
by: Nguyen, Kien Huu
Published: (2023)

Geometric condition for Dependent Choice
by: Karagila, Asaf, et al.
Published: (2022)