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Diophantine equations defined by binary quadratic forms over rational function fields

Volume 196 / 2020

Chang Lv Acta Arithmetica 196 (2020), 35-51 MSC: Primary 11E12, 11D57, 11R58; Secondary 14L30, 11R37. DOI: 10.4064/aa190404-8-12 Published online: 10 June 2020


We study the “imaginary” binary quadratic form equations $ax^2+bxy+cy^2+g=0$ over $k[t]$ in rational function fields, showing that a condition on the Artin reciprocity map is the only obstruction to the local-global principle for integral solutions of the equation.


  • Chang LvState Key Laboratory of Information Security
    Institute of Information Engineering
    Chinese Academy of Sciences
    Beijing 100093, P.R. China

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