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 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 Hermitian Forms.
On the classification of hermitian forms. I. Rings of algebraic integers
On the classification of Hilbert Modular threefolds.
On the class-number of the maximal real subfield of a cyclotomic field.
On the coefficients of Drinfeld modular forms.
On the cohomology of biquadratic extensions.
On the common index divisors of a dihedral field of prime degree.
On the composite Lehmer numbers with prime indices, III
On the compositum of all degree extensions of a number field
We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of Bombieri and...
On the computation of Hermite-Humbert constants for real quadratic number fields
We present algorithms for the computation of extreme binary Humbert forms in real quadratic number fields. With these algorithms we are able to compute extreme Humbert forms for the number fields and . Finally we compute the Hermite-Humbert constant for the number field .
On the computation of quadratic -class groups
We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer mod and the factorization of , computes the structure of the -Sylow subgroup of the class group of the quadratic order of discriminant in random polynomial time in .
On the computation of the class numbers of some cubic fields.
On the conductor discriminant formula.
On the conductor of the Jacobi sum Hecke character
On the congruence , where q is a prime and f is a polynomial