Displaying similar documents to “On the n -torsion subgroup of the Brauer group of a number field”

Boundedness results of solutions to the equation x ′′′ + a x ′′ + g ( x ) x + h ( x ) = p ( t ) without the hypothesis h ( x ) sgn x 0 f o r | x | > R .

Ján Andres (1986)

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

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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ( x ) sgn x 0 f o r | x | > R , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

On the ring of p -integers of a cyclic p -extension over a number field

Humio Ichimura (2005)

Journal de Théorie des Nombres de Bordeaux

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Let p be a prime number. A finite Galois extension N / F of a number field F with group G has a normal p -integral basis ( p -NIB for short) when 𝒪 N is free of rank one over the group ring 𝒪 F [ G ] . Here, 𝒪 F = 𝒪 F [ 1 / p ] is the ring of p -integers of F . Let m = p e be a power of p and N / F a cyclic extension of degree m . When ζ m F × , we give a necessary and sufficient condition for N / F to have a p -NIB (Theorem 3). When ζ m F × and p [ F ( ζ m ) : F ] , we show that N / F has a p -NIB if and only if N ( ζ m ) / F ( ζ m ) has a p -NIB (Theorem 1). When p divides [ F ( ζ m ) : F ] , we show that this...

Boundedness results of solutions to the equation x ′′′ + a x ′′ + g ( x ) x + h ( x ) = p ( t ) without the hypothesis h ( x ) sgn x 0 for | x | > R .

Ján Andres (1986)

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

Similarity:

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ( x ) sgn x 0 f o r | x | > R , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

Quaternion extensions with restricted ramification

Peter Schmid (2014)

Acta Arithmetica

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In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime p 1 ( m o d 2 n - 1 ) , there exist unique real and complex...

On sets which contain a qth power residue for almost all prime modules

Mariusz Ska/lba (2005)

Colloquium Mathematicae

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A classical theorem of M. Fried [2] asserts that if non-zero integers β , . . . , β l have the property that for each prime number p there exists a quadratic residue β j mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

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Let f ( X ) [ X ] be a monic polynomial which is a power of a polynomial g ( X ) [ X ] of degree μ 2 and having simple real roots. For given positive integers d 1 , d 2 , , m with < m and gcd ( , m ) = 1 with μ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) f ( x + ( k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) 0 for 0 j < k has only finitely many solutions in integers x , y and k 1 except in the case m = μ = 2 , = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .

Making sense of capitulation: reciprocal primes

David Folk (2016)

Acta Arithmetica

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Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and a any generator of the principal ideal . We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates G a l ( K ( a ) / K ) for every choice of a . We then show that becomes principal in L if and only if every reciprocal prime is not...

Galois co-descent for étale wild kernels and capitulation

Manfred Kolster, Abbas Movahhedi (2000)

Annales de l'institut Fourier

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Let F be a number field with ring of integers o F . For a fixed prime number p and i 2 the étale wild kernels W K 2 i - 2 e ´ t ( F ) are defined as kernels of certain localization maps on the i -fold twist of the p -adic étale cohomology groups of spec o F [ 1 p ] . These groups are finite and coincide for i = 2 with the p -part of the classical wild kernel W K 2 ( F ) . They play a role similar to the p -part of the p -class group of F . For class groups, Galois co-descent in a cyclic extension L / F is described by the ambiguous class formula given...

Pure fields of degree 9 with class number prime to 3

Colin D. Walter (1980)

Annales de l'institut Fourier

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The main theorem gives necessary conditions and sufficient conditions for Q ( n 9 ) to have class number prime to 3. These conditions involve only the rational prime factorization of n and congruences mod 27 of the prime factors of n . They give necessary and sufficient conditions for most n .