The non-abelian normal CM-fields of degree 36 with class number one
The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent
The number of real quadratic fields having units of negative norm.
The number of S₄-fields with given discriminant
The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders
Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.
The reduced ideals of a special order in a pure cubic number field
Let be a pure cubic field, with , where is a cube-free integer. We will determine the reduced ideals of the order of which coincides with the maximal order of in the case where is square-free and .
The Regulator Spectrum For Totally Real Cubic Fields.
The Stickelberger element of an imaginary quadratic field
The totally real extension of degree 6 with minimum discriminant.
The totally real extension of degree 6 with minimum discriminant.
The unit group of some fields of the form
Let and be two different prime integers such that with , and a positive odd square-free integer relatively prime to and . In this paper we investigate the unit groups of number fields .
The χ-part of the Analytic Class Number Formula, for Global Function Fields
Let F/k be a finite abelian extension of global function fields, totally split at a distinguished place ∞ of k. We show that a complex Gras conjecture holds for Stark units, and we derive a refined analytic class number formula.
Theoretical evidence in support of the extended abelian rank one Stark conjecture for the base field ℚ
Theta series associated with certain positive definite binary quadratic forms
Recently, P. C. Toh derived identities expressing theta series associated with fundamental idoneal discriminants in terms of generalized Lambert series. His method depends on the fact that the ring of integers of a number field is a Dedekind domain, and is not applicable to theta series associated with non-fundamental idoneal discriminants. The aim of this article is to devise methods for determining the generalized Lambert series representations of theta series associated with non-fundamental idoneal...
Trace formulae and imaginary quadratic fields.
Über die Anzahl der Ideal-Classen in den verschiedenen Ordnungen eines endlichen Körpers [Book]
Über die arithmetischen Eigenschaften der algebraischen und transzendenten Zahlen.
Über die außerwesentlichen Diskriminantenteiler einer Gattung.
Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
Über die Classenzahl quadratischer Zahlkörper