Displaying similar documents to “Permuting the partitions of a prime”

Kloosterman sums for prime powers in -adic fields

Stanley J. Gurak (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let K be a field of degree n over Q p , the field of rational p -adic numbers, say with residue degree f , ramification index e and differential exponent d . Let O be the ring of integers of K and P its unique prime ideal. The trace and norm maps for K / Q p are denoted T r and N , respectively. Fix q = p r , a power of a prime p , and let η be a numerical character defined modulo q and of order o ( η ) . The character η extends to the ring of p -adic integers p in the natural way; namely η ( u ) = η ( u ˜ ) , where u ˜ denotes the residue...

On the trace of the ring of integers of an abelian number field

Kurt Girstmair (1992)

Acta Arithmetica

Similarity:

Let K, L be algebraic number fields with K ⊆ L, and O K , O L their respective rings of integers. We consider the trace map T = T L / K : L K and the O K -ideal T ( O L ) O K . By I(L/K) we denote the group indexof T ( O L ) in O K (i.e., the norm of T ( O L ) over ℚ). It seems to be difficult to determine I(L/K) in the general case. If K and L are absolutely abelian number fields, however, we obtain a fairly explicit description of the number I(L/K). This is a consequence of our description of the Galois module structure of T ( O L ) (Theorem 1)....

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

Similarity:

1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a p -extension of k, k n the nth layer of k / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k / k be a p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k / k . Then there exist integers λ = λ ( k / k ) 0 , μ = μ ( k / k ) 0 , ν = ν ( k / k ) , and n₀ ≥ 0...

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

Topological structure of the space of lower semi-continuous functions

Katsuro Sakai, Shigenori Uehara (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let L ( X ) be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space X , where, by identifying each f with the epi-graph epi ( f ) , L ( X ) is regarded the subspace of the space Cld F * ( X × ) of all closed sets in X × with the Fell topology. Let LSC ( X ) = { f L ( X ) f ( X ) , f ( X ) ( - , ] } and LSC B ( X ) = { f L ( X ) f ( X ) is a bounded subset of } . We show that L ( X ) is homeomorphic to the Hilbert cube Q = [ - 1 , 1 ] if and only if X is second countable, locally compact and infinite. In this case, it is proved that ( L ( X ) , LSC ( X ) , LSC B ( X ) ) is homeomorphic to ( Cone Q , Q × ( 0 , 1 ) , Σ × ( 0 , 1 ) ) (resp. ( Q , s , Σ ) ) if X is compact (resp. X is non-compact), where Cone Q = ( Q × 𝐈 ) / ( Q × { 1 } ) is...