Displaying similar documents to “Corrigendum to 'Norm residue symbol and cyclotomic units' (Acta Arith. 73 (1995), 147-188)”

On the magnitudes of some small cyclotomic integers

Frederick Robinson, Michael Wurtz (2013)

Acta Arithmetica

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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...

On the class numbers of real cyclotomic fields of conductor pq

Eleni Agathocleous (2014)

Acta Arithmetica

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The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields...

On the ordinarity of the maximal real subfield of cyclotomic function fields

Daisuke Shiomi (2014)

Acta Arithmetica

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The aim of this paper is to clarify the ordinarity of cyclotomic function fields. In the previous work [J. Number Theory 133 (2013)], the author determined all monic irreducible polynomials m such that the maximal real subfield of the mth cyclotomic function field is ordinary. In this paper, we extend this result to the general case.

A note on circular units in ℤ p -extensions

Radan Kučera (2003)

Journal de théorie des nombres de Bordeaux

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In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic ℤ p -extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.