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Regulators and total positivity.

Eduardo Friedman (2007)

Publicacions Matemàtiques

[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

Regulators of rank one quadratic twists

Christophe Delaunay, Xavier-François Roblot (2008)

Journal de Théorie des Nombres de Bordeaux

We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators. We also describe an efficient algorithm to compute explicitly some of the invariants of a rank one quadratic twist of an elliptic curve (regulator, order of the Tate-Shafarevich group, etc.) and we discuss the numerical data that we obtain and compare it with our predictions.

Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes

Yuichi Kamiya, Leo Murata (2012)

Journal de Théorie des Nombres de Bordeaux

In the study of the 2 -adic sum of digits function S 2 ( n ) , the arithmetical function u ( 0 ) = 0 and u ( n ) = ( - 1 ) n - 1 for n 1 plays a very important role. In this paper, we firstly generalize the relation between S 2 ( n ) and u ( n ) to a bijective relation between arithmetical functions. And as an application, we investigate some aspects of the sum of digits functions S 𝒢 ( n ) induced by binary infinite Gray codes 𝒢 . We can show that the difference of the sum of digits function, S 𝒢 ( n ) - S 𝒢 ( n - 1 ) , is realized by an automaton. And the summation formula of the sum...

Relations between Elements r p l - r and p·1 for a Prime p

Andrzej Prószyński (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

For any positive power n of a prime p we find a complete set of generating relations between the elements [r] = rⁿ - r and p·1 of a unitary commutative ring.

Relations between jacobians of modular curves of level p 2

Imin Chen, Bart De Smit, Martin Grabitz (2004)

Journal de Théorie des Nombres de Bordeaux

We derive a relation between induced representations on the group GL 2 ( / p 2 ) which implies a relation between the jacobians of certain modular curves of level p 2 . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( / p 2 ) .

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