Studying Hilbert’s 10th problem via explicit elliptic curves

Authors

Debanjana Kundu, The University of Texas Rio Grande Valley
Antonio Lei
Florian Sprung

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

Reprints and permissions

https://rdcu.be/dNZPg

Recommended Citation

Kundu, D., Lei, A. & Sprung, F. Studying Hilbert’s 10th problem via explicit elliptic curves. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02879-9

Publication Title

Mathematische Annalen

DOI

10.1007/s00208-024-02879-9