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On computations with integer division

Bettina Just, Friedhelm Meyer auf der Heide, Avi Wigderson (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

On lattice bases with special properties

Ulrich Halbritter, Michael E. Pohst (2000)

Journal de théorie des nombres de Bordeaux

In this paper we introduce multiplicative lattices in ( > 0 ) r and determine finite unions of suitable simplices as fundamental domains for sublattices of finite index. For this we define cyclic non-negative bases in arbitrary lattices. These bases are then used to calculate Shintani cones in totally real algebraic number fields. We mainly concentrate our considerations to lattices in two and three dimensions corresponding to cubic and quartic fields.

On the magnitudes of some small cyclotomic integers

Frederick Robinson, Michael Wurtz (2013)

Acta Arithmetica

We prove the last of five outstanding conjectures made by R. M. Robinson from 1965 concerning small cyclotomic integers. In particular, given any cyclotomic integer β all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of one of four explicit types given by two infinite classes and two exceptional cases. We also extend this result by showing that with the addition of one form, the conjecture is true for β with magnitudes up to 5 + 1/25....

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