2023 -CURVES, HECKE CHARACTERS, AND SOME DIOPHANTINE EQUATIONS II
Ariel Pacetti, Lucas Villagra Torcomian
Author Affiliations +
Publ. Mat. 67(2): 569-599 (2023). DOI: 10.5565/PUBLMAT6722304

Abstract

In the article [25] a general procedure to study solutions of the equations x4dy2=zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension (d,ϵ)/(d) (where ϵ is a fundamental unit) needed to prove the existence of a Hecke character over (d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from -curves from imaginary to real quadratic fields.

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Ariel Pacetti. Lucas Villagra Torcomian. "-CURVES, HECKE CHARACTERS, AND SOME DIOPHANTINE EQUATIONS II." Publ. Mat. 67 (2) 569 - 599, 2023. https://doi.org/10.5565/PUBLMAT6722304

Information

Received: 22 March 2021; Revised: 25 March 2022; Published: 2023
First available in Project Euclid: 29 June 2023

MathSciNet: MR4609012
zbMATH: 07720471
Digital Object Identifier: 10.5565/PUBLMAT6722304

Subjects:
Primary: 11D41 , 11F80

Keywords: Diophantine equations , ℚ-curves

Rights: Copyright © 2023 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.67 • No. 2 • 2023
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