All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 101

Showing per page

Analytic normal basis theorem

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu (2008)

Open Mathematics

Let p be a prime number, ℚp the field of p-adic numbers, and ℚ ¯ p a fixed algebraic closure of ℚp. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚp ⊆ K ⊆ L ⊆ ℚ ¯ p .

Analytic potential theory over the p -adics

Shai Haran (1993)

Annales de l'institut Fourier

Over a non-archimedean local field the absolute value, raised to any positive power α > 0 , is a negative definite function and generates (the analogue of) the symmetric stable process. For α ∈ ( 0 , 1 ) , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.

Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme

Philippe Cassou-Noguès (1981)

Annales de l'institut Fourier

Nous étudions les fonctions p -adiques associées à des séries du type Z ( P , Q , ξ ) ( s ) = ∑ n ∈ N r Q ( n ) ξ n P ( n ) - s dans certains cas, où elles admettent un prolongement méromorphe à C avec un nombre fini de pôles et des valeurs aux entiers négatifs algébriques. On retrouve comme cas particulier les fonctions L p -adiques des corps totalement réels et les fonctions Γ -multiples p -adiques.

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

Fix an integer ℓ ≥ 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order ℓ , where K satisfies some mild hypotheses. In this paper we define the family of generalized Rikuna polynomials { r n ( x , t ) } n ≥ 1 of degree ℓ n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd ℓ over an arbitrary base field and give applications to arithmetic dynamical systems.

Associated orders of certain extensions arising from Lubin-Tate formal groups

Nigel P. Byott (1997)

Journal de théorie des nombres de Bordeaux

Let k be a finite extension of ℚ p , let k 1 , respectively k 3 , be the division fields of level 1 , respectively 3 , arising from a Lubin-Tate formal group over k , and let Γ = Gal( k 3 / k 1 ). It is known that the valuation ring k 3 cannot be free over its associated order 𝔄 in K Γ unless k = ℚ p . We determine explicitly under the hypothesis that the absolute ramification index of k is sufficiently large.

Currently displaying 81 – 100 of 101