Displaying similar documents to “Prime factors of class number of cyclotomic fields”

On the generalized principal ideal theorem of complex multiplication

Reinhard Schertz (2006)

Journal de Théorie des Nombres de Bordeaux

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In the p n -th cyclotomic field p n , p a prime number, n , the prime p is totally ramified and the only ideal above p is generated by ω n = ζ p n - 1 , with the primitive p n -th root of unity ζ p n = e 2 π i p n . Moreover these numbers represent a norm coherent set, i.e. N p n + 1 / p n ( ω n + 1 ) = ω n . It is the aim of this article to establish a similar result for the ray class field K 𝔭 n of conductor 𝔭 n over an imaginary quadratic number field K where 𝔭 n is the power of a prime ideal in K . Therefore the exponential function has to be replaced by a suitable elliptic...

Equidistribution in the dual group of the S -adic integers

Roman Urban (2014)

Czechoslovak Mathematical Journal

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Let X be the quotient group of the S -adele ring of an algebraic number field by the discrete group of S -integers. Given a probability measure μ on X d and an endomorphism T of X d , we consider the relation between uniform distribution of the sequence T n 𝐱 for μ -almost all 𝐱 X d and the behavior of μ relative to the translations by some rational subgroups of X d . The main result of this note is an extension of the corresponding result for the d -dimensional torus 𝕋 d due to B. Host.

Positive solutions for systems of generalized three-point nonlinear boundary value problems

Johnny Henderson, Sotiris K. Ntouyas, Ioannis K. Purnaras (2008)

Commentationes Mathematicae Universitatis Carolinae

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Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u ' ' + λ a ( t ) f ( v ) = 0 , v ' ' + λ b ( t ) g ( u ) = 0 , for 0 < t < 1 , and satisfying, u ( 0 ) = β u ( η ) , u ( 1 ) = α u ( η ) , v ( 0 ) = β v ( η ) , v ( 1 ) = α v ( η ) . A Guo-Krasnosel’skii fixed point theorem is applied.

Linear extensions of relations between vector spaces

Árpád Száz (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let X and Y be vector spaces over the same field K . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λ F ( x ) F ( λ x ) and F ( x ) + F ( y ) F ( x + y ) for all λ K { 0 } and x , y X . After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X into Y can be extended to a linear relation F of X into Y if and only if there exists a linear subspace Z of Y such that Φ ( e ) Y | Z for all e E . Moreover, if...