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On the structure of Milnor K -groups of certain complete discrete valuation fields

Masato Kurihara (2004)

Journal de Théorie des Nombres de Bordeaux

For a typical example of a complete discrete valuation field K of type II in the sense of [12], we determine the graded quotients gr i K 2 ( K ) for all i > 0 . In the Appendix, we describe the Milnor K -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.

On the structure of sequences with forbidden zero-sum subsequences

W. D. Gao, R. Thangadurai (2003)

Colloquium Mathematicae

We study the structure of longest sequences in d which have no zero-sum subsequence of length n (or less). We prove, among other results, that for n = 2 a and d arbitrary, or n = 3 a and d = 3, every sequence of c(n,d)(n-1) elements in d which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where c ( 2 a , d ) = 2 d and c ( 3 a , 3 ) = 9 .

On the structure of sets with small doubling property on the plane (I)

Yonutz Stanchescu (1998)

Acta Arithmetica

Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.

On the structure of the 2-Iwasawa module of some number fields of degree 16

Idriss Jerrari, Abdelmalek Azizi (2022)

Czechoslovak Mathematical Journal

Let K be an imaginary cyclic quartic number field whose 2-class group is of type ( 2 , 2 , 2 ) , i.e., isomorphic to / 2 × / 2 × / 2 . The aim of this paper is to determine the structure of the Iwasawa module of the genus field K ( * ) of K .

On the structure of the Galois group of the Abelian closure of a number field

Georges Gras (2014)

Journal de Théorie des Nombres de Bordeaux

From a paper by A. Angelakis and P. Stevenhagen on the determination of a family of imaginary quadratic fields K having isomorphic absolute Abelian Galois groups A K , we study any such issue for arbitrary number fields K . We show that this kind of property is probably not easily generalizable, apart from imaginary quadratic fields, because of some p -adic obstructions coming from the global units of K . By restriction to the p -Sylow subgroups of A K and assuming the Leopoldt conjecture we show that the...

On the structure of (−β)-integers

Wolfgang Steiner (2012)

RAIRO - Theoretical Informatics and Applications

The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. When β is the analogue of a Parry number, we describe the structure of the set of (−β)-integers by a fixed point of an anti-morphism.

On the subfields of cyclotomic function fields

Zhengjun Zhao, Xia Wu (2013)

Czechoslovak Mathematical Journal

Let K = 𝔽 q ( T ) be the rational function field over a finite field of q elements. For any polynomial f ( T ) 𝔽 q [ T ] with positive degree, denote by Λ f the torsion points of the Carlitz module for the polynomial ring 𝔽 q [ T ] . In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield M of the cyclotomic function field K ( Λ P ) of degree k over 𝔽 q ( T ) , where P 𝔽 q [ T ] is an irreducible polynomial of positive degree and k > 1 is a positive divisor of q - 1 . A formula for the analytic class number for the...

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