Congruent numbers over real number fields

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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On the indices of multiquadratic number fields

Attila Pethő, Michael E. Pohst (2012)

Acta Arithmetica

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Distribution of the traces of Frobenius on elliptic curves over function fields

Amílcar Pacheco (2003)

Acta Arithmetica

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Roth's theorem on systems of linear forms in function fields

Yu-Ru Liu, Craig V. Spencer, Xiaomei Zhao (2010)

Acta Arithmetica

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Waring's Problem for Fields

W. J. Ellison (1970-1971)

Séminaire de théorie des nombres de Bordeaux

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A note on Waring's problem in finite fields

Arne Winterhof (2001)

Acta Arithmetica

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Points on elliptic curves over finite fields

M. Skałba (2005)

Acta Arithmetica

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On Artin $L$ -functions for octic quaternion fields.

Omar, Sami (2001)

Experimental Mathematics

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Fields: Algebraically closed and others.

Paulo Ribenboim (1992)

Manuscripta mathematica

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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...