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Displaying similar documents to “Congruent numbers over real number fields”

Obituary: Vasyl Ivanovych Andriychuk (18.09.1948–7.07.2012)

Taras Banakh, Fedor Bogomolov, Andrij Gatalevych, Ihor Guran, Yurij Ishchuk, Mykola Komarnytskyi, Igor Kuz, Ivanna Melnyk, Vasyl Petrychkovych, Yaroslav Prytula, Oleh Romaniv, Oleh Skaskiv, Ludmyla Stakhiv, Georgiy Sullym, Bohdan Zabavskyi, Volodymir Zelisko, Mykhajlo Zarichnyi (2013)

Open Mathematics

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Heights and regulators of number fields and elliptic curves

Fabien Pazuki (2014)

Publications mathématiques de Besançon

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We compare general inequalities between invariants of number fields and invariants of elliptic curves over number fields. On the number field side, we remark that there is only a finite number of non-CM number fields with bounded regulator. On the elliptic curve side, assuming the height conjecture of Lang and Silverman, we obtain a Northcott property for the regulator on the set of elliptic curves with dense rational points over a number field. This amounts to say that the arithmetic...