On some new estimates for h¯(ℚ(ζₚ))
Stanislav Jakubec (2009)
Acta Arithmetica
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Displaying similar documents to “A congruence for the second factor of the class number of a cyclotomic field (Corrigendum)”
On some new estimates for h¯(ℚ(ζₚ))
On an equation in cyclotomic numbers
Roberto Dvornicich (2001)
Acta Arithmetica
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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.
On the relative class number of cyclotomic function fields
Hwanyup Jung, Jaehyun Ahn (2003)
Acta Arithmetica
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A determinant formula for congruence zeta functions of maximal real cyclotomic function fields
Daisuke Shiomi (2009)
Acta Arithmetica
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Class numbers of cyclotomic function fields
Sunghan Bae, Pyung-Lyun Kang (2002)
Acta Arithmetica
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On the class numbers of cyclotomic fields.
Kuniaki Horie (1989)
Manuscripta mathematica
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Congruence of Ankeny-Artin-Chowla type for cyclic fields
Stanislav Jakubec (1998)
Mathematica Slovaca
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On the size of the first factor of the class number of a cyclotomic field.
A. Granville (1990)
Inventiones mathematicae
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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 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 ray class annihilators of cyclotomic function fields
Sunghan Bae, Hwanyup Jung (2011)
Acta Arithmetica
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A q-analogue of Lehmer's congruence
Hao Pan (2007)
Acta Arithmetica
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Corrigendum to "Norm residue symbol and cyclotomic units" (Acta Arith. 73 (1995), 147-188)
Charles Helou (2001)
Acta Arithmetica
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On the integral basis of the maximal real subfield of a cyclotomic field.
Joseph J. Liang (1976)
Journal für die reine und angewandte Mathematik
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Class numbers of totally real fields and applications to the Weber class number problem
John C. Miller (2014)
Acta Arithmetica
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The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application...