School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Article

Publication Date

5-6-2024

Abstract

N. García-Fritz and H. Pasten showed that Hilbert’s 10th problem is unsolvable in the ring of integers of number fields of the form Q(p–√3,−q−−−√) for positive proportions of primes p and q. We improve their proportions and extend their results to the case of number fields of the form Q(p–√3,Dq−−−√) , where D belongs to an explicit family of positive square-free integers. We achieve this by using multiple elliptic curves, and replace their Iwasawa theory arguments by a more direct method.

Comments

Original published version available at https://rdcu.be/dNZPg

Publication Title

Mathematische Annalen

DOI

10.1007/s00208-024-02879-9

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 1
  • Usage
    • Downloads: 8
    • Abstract Views: 5
see details

Included in

Mathematics Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.