On the trace map between absolutely abelian number fields of equal conductor
On the trace of the ring of integers of an abelian number field
Let K, L be algebraic number fields with K ⊆ L, and , their respective rings of integers. We consider the trace map and the -ideal . By I(L/K) we denote the group indexof in (i.e., the norm of 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 (Theorem 1). The case...
On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
Lately, explicit upper bounds on (for primitive Dirichlet characters ) taking into account the behaviors of on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds of relative class numbers of CM-fields whose maximal totally real subfields are abelian. We present here some other...
On the values of equivariant zeta functions of curves over finite fields.
On the vanishing of Iwasawa invariants of absolutely abelian p-extensions
1. Introduction. Let p be a prime number and the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, a -extension of k, the nth layer of , and the p-Sylow subgroup of the ideal class group of . Iwasawa proved the following well-known theorem about the order of : Theorem A (Iwasawa). Let be a -extension and the p-Sylow subgroup of the ideal class group of , where is the th layer of . Then there exist integers , , , and n₀ ≥ 0 such that for...
On the vanishing of Iwasawa invariants of geometric cyclotomic ℤₚ-extensions
On the verification of Clark's example of a euclidean but not norm-euclidean number field.
On the zeros of a class of L-functions
On the zeros of Hecke's L-functions III
On the Zeta Function of Number Fields.
On the -expansion of an algebraic number in an algebraic base .
On the µ-invariants of cyclotomic fields
On theta functions of real algebraic number fields
On totally real Hilbert-Speiser fields of type Cₚ
On traces of the Brandt-Eichler matrices
We compute the numbers of locally principal ideals with given norm in a class of definite quaternion orders and the traces of the Brandt-Eichler matrices corresponding to these orders. As an application, we compute the numbers of representations of algebraic integers by the norm forms of definite quaternion orders with class number one as well as we obtain class number relations for some CM-fields.
On twisted Galois-Gauß sums and canonical factorizations.
On two problems of E. M. Robinson about sums of roots of unity
On two-primary algebraic K-theory of quadratic number rings with focus on K₂
On type numbers of split orders of definite quaternion algebras.
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field