Displaying similar documents to “On units of some fields of the form ( 2 , p , q , - l )

The unit group of some fields of the form ( 2 , p , q , - l )

Moha Ben Taleb El Hamam (2024)

Mathematica Bohemica

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Let p and q be two different prime integers such that p q 3 ( mod 8 ) with ( p / q ) = 1 , and l a positive odd square-free integer relatively prime to p and q . In this paper we investigate the unit groups of number fields 𝕃 = ( 2 , p , q , - l ) .

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ¯ b to the extendability of C R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results...

Note on the Hilbert 2-class field tower

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2022)

Mathematica Bohemica

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Let k be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields 𝕜 = ( d , - 1 ) , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).

Bicyclotomic polynomials and impossible intersections

David Masser, Umberto Zannier (2013)

Journal de Théorie des Nombres de Bordeaux

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In a recent paper we proved that there are at most finitely many complex numbers t 0 , 1 such that the points ( 2 , 2 ( 2 - t ) ) and ( 3 , 6 ( 3 - t ) ) are both torsion on the Legendre elliptic curve defined by y 2 = x ( x - 1 ) ( x - t ) . In a sequel we gave a generalization to any two points with coordinates algebraic over the field Q ( t ) and even over C ( t ) . Here we reconsider the special case ( u , u ( u - 1 ) ( u - t ) ) and ( v , v ( v - 1 ) ( v - t ) ) with complex numbers u and v .

On analytic rapidly decreasing functions of a real variable

Gianfranco Cimmino (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Condizione necessaria e sufficiente affinché una funzione rapidamente decrescente di variabile reale sia uniformemente analitica è che per i suoi coefficienti γ 0 , γ 1 , di Fourier-Hermite riesca γ m = 0 ( e m t ) per t > 0 abbastanza piccolo.

Run-length function of the Bolyai-Rényi expansion of real numbers

Rao Li, Fan Lü, Li Zhou (2024)

Czechoslovak Mathematical Journal

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By iterating the Bolyai-Rényi transformation T ( x ) = ( x + 1 ) 2 ( mod 1 ) , almost every real number x [ 0 , 1 ) can be expanded as a continued radical expression x = - 1 + x 1 + x 2 + + x n + with digits x n { 0 , 1 , 2 } for all n . For any real number x [ 0 , 1 ) and digit i { 0 , 1 , 2 } , let r n ( x , i ) be the maximal length of consecutive i ’s in the first n digits of the Bolyai-Rényi expansion of x . We study the asymptotic behavior of the run-length function r n ( x , i ) . We prove that for any digit i { 0 , 1 , 2 } , the Lebesgue measure of the set D ( i ) = x [ 0 , 1 ) : lim n r n ( x , i ) log n = 1 log θ i is 1 , where θ i = 1 + 4 i + 1 . We also obtain that the level set E α ( i ) = x [ 0 , 1 ) : lim n r n ( x , i ) log n = α is of full Hausdorff...

The operation A B A in operator algebras

Marcell Gaál (2020)

Commentationes Mathematicae Universitatis Carolinae

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The binary operation a b a , called Jordan triple product, and its variants (such as e.g. the sequential product a b a or the inverted Jordan triple product a b - 1 a ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.

On the Hilbert 2 -class field tower of some imaginary biquadratic number fields

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini, Idriss Jerrari (2021)

Czechoslovak Mathematical Journal

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Let 𝕜 = 2 , d be an imaginary bicyclic biquadratic number field, where d is an odd negative square-free integer and 𝕜 2 ( 2 ) its second Hilbert 2 -class field. Denote by G = Gal ( 𝕜 2 ( 2 ) / 𝕜 ) the Galois group of 𝕜 2 ( 2 ) / 𝕜 . The purpose of this note is to investigate the Hilbert 2 -class field tower of 𝕜 and then deduce the structure of G .

Lower bound for class numbers of certain real quadratic fields

Mohit Mishra (2023)

Czechoslovak Mathematical Journal

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Let d be a square-free positive integer and h ( d ) be the class number of the real quadratic field ( d ) . We give an explicit lower bound for h ( n 2 + r ) , where r = 1 , 4 . Ankeny and Chowla proved that if g > 1 is a natural number and d = n 2 g + 1 is a square-free integer, then g h ( d ) whenever n > 4 . Applying our lower bounds, we show that there does not exist any natural number n > 1 such that h ( n 2 g + 1 ) = g . We also obtain a similar result for the family ( n 2 g + 4 ) . As another application, we deduce some criteria for a class group of prime power order to be...

On the strongly ambiguous classes of some biquadratic number fields

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Mathematica Bohemica

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We study the capitulation of 2 -ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields 𝕜 = ( 2 p q , i ) , where i = - 1 and p - q 1 ( mod 4 ) are different primes. For each of the three quadratic extensions 𝕂 / 𝕜 inside the absolute genus field 𝕜 ( * ) of 𝕜 , we determine a fundamental system of units and then compute the capitulation kernel of 𝕂 / 𝕜 . The generators of the groups Am s ( 𝕜 / F ) and Am ( 𝕜 / F ) are also determined from which we deduce that 𝕜 ( * ) is smaller than the relative genus field ( 𝕜 / ( i ) ) * . Then we prove...