On the class number of binary quadratic forms: An omega estimate for the error term.
On the class number of relative abelian fields.
On the class number of some real abelian number fields of prime conductors
On the class number of the maximal real subfields of a family of cyclotomic fields
For any square-free positive integer with , we prove that the class number of the real cyclotomic field is greater than , where is a primitive th root of unity.
On the class number Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime
On the class numbers of certain Hilbert class fields.
On the class numbers of certain quadratic extensions
On the class numbers of cyclotomic fields.
On the class numbers of Q(√±2p) modulo 16, for p ≡ 1 (mod 8) a prime
On the class numbers of real cyclotomic fields of conductor pq
The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields of prime...
On the class of all reciprocal bases for integers.
On the classgroups of imaginary abelian fields
Let be an odd prime, an odd, -adic Dirichlet character and the cyclic imaginary extension of associated to . We define a “-part” of the Sylow -subgroup of the class group of and prove a result relating its -divisibility to that of the generalized Bernoulli number . This uses the results of Mazur and Wiles in Iwasawa theory over . The more difficult case, in which divides the order of is our chief concern. In this case the result is new and confirms an earlier conjecture of G....
On the classification of 3-dimensional non-associative division algebras over -adic fields
Let be a prime and a -adic field (a finite extension of the field of -adic numbers ). We employ the main results in [12] and the arithmetic of elliptic curves over to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over to the classification of ternary cubic forms over (up to equivalence) with no non-trivial zeros over . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...
On the Classification of Hermitian Forms.
On the classification of hermitian forms. I. Rings of algebraic integers
On the Classification of Hermitian Forms. III. Complete Semilocal Rings.
On the classification of Hilbert Modular threefolds.
On the classification of quadratic forms over semi local rings
On the class-number of the maximal real subfield of a cyclotomic field.
On the closed subfields of [...] Q ¯ p
Let p be a prime number, and let [...] Q¯ p be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.