The Adelic Zeta Function Associated to the Space of Binary Cubis Forms. Part I: Global Theory.
The adelic zeta function associated to the space of binary cubic forms. II: Local theory.
The annihilation of divisor classes in abelian extensions of the rational function field
The Approximation of Solutions to Linear Homogeneous Differential Equations by Rational Functions.
The Arithmetic Genus of the Hubert Modular Variety and the Elliptic Fixed Points of the Hilbert Modular Group.
The arithmetic of function fields
The Bloch-Kato conjecture on special values of -functions. A survey of known results
This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.
The Bloch-Wigner-Ramakrishnan polylogarithm function.
The Brauer-Kuroda formula for higher S-class numbers in dihedral extensions of number fields
The Brauer-Siegel theorem for algebraic function fields.
The calculation of large units in cyclic cubic fields.
The catenary degree of Krull monoids I
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree of is the smallest integer with the following property: for each and each two factorizations of , there exist factorizations of such that, for each , arises from by replacing at most atoms from by at most new atoms. Under a very mild condition...
The Cebotarev Density Theorem for Function Fields: An Elementary Approach.
The Chowla-Selberg formula for genera
The circular units and the Stickelberger ideal of a cyclotomic field revisited
The aim of this paper is a new construction of bases of the group of circular units and of the Stickelberger ideal for a family of abelian fields containing all cyclotomic fields, namely for any compositum of imaginary abelian fields, each ramified only at one prime. In contrast to the previous papers on this topic our approach consists in an explicit construction of Ennola relations. This gives an explicit description of the torsion parts of odd and even universal ordinary distributions, but it...
The Class Number of Hereditary Orders in Non-Eichler Algebras over Global Fuction Fields.
The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer
The class number one problem for some non-abelian normal CM-fields of degree
We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .
The class number one problem for the dihedral and dicyclic CM-fields
We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.
The class number one problem for the non-abelian normal CM-fields of degree 16